I can confirm the described faulty behaviour both under Fedora 32 and Fedora 33.

I also confirm the following two lines in the log output, when the connection to the coupled device failes:

remote_... 2020.11.10 14:53:58.560 97511 C ConnectRequest::ConnectRequest(remote_device/RemoteConnectorImpl.cpp:192)  : Start reconnect to server
remote_... 2020.11.10 14:53:58.713 97511 W ConnectRequest::onError(remote_device/RemoteConnectorImpl.cpp:111)         : Connection error: QAbstractSocket::SocketError(13)

I also build a custom AlpineLinux based Podman image (based on https://github.com/misery/DockerAusweisApp2). Using this I do not encounter the problem. 
I hazard the conjecture that the underlying reason might be some incompatibility with Fedora's OpenSSL or QT libraries.

I can confirm the behaviour described above.

System: Fedora 33

$ rpm -q AusweisApp2
AusweisApp2-1.20.2-9.fc33.x86_64

In the terminal I receive the following error messages:

remote_... 2020.11.12 11:09:46.409 10409 C ConnectRequest::ConnectRequest(remote_device/RemoteConnectorImpl.cpp:192)  : Start reconnect to server
remote_... 2020.11.12 11:09:46.534 10409 W ConnectRequest::onError(remote_device/RemoteConnectorImpl.cpp:111)         : Connection error: QAbstractSocket::SocketError(13)

Happy to help testing if needed.

FYI, the flatpak from flathub.org comes with more than 1.5 GB of KDE dependencies. For that reason I did not test the flatpak, but maybe this information helps with troubleshooting.

$ flatpak install flathub de.bund.ausweisapp.ausweisapp2
Looking for matches…
Required runtime for de.bund.ausweisapp.ausweisapp2/x86_64/stable (runtime/org.kde.Platform/x86_64/5.15) found in remote flathub
Do you want to install it? [Y/n]: Y

de.bund.ausweisapp.ausweisapp2 permissions:
    network               fallback-x11     pcsc               wayland
    x11                   dri              file access [1]    dbus access [2]
    bus ownership [3]

    [1] xdg-config/kdeglobals:ro
    [2] com.canonical.AppMenu.Registrar, org.freedesktop.Notifications,
        org.kde.StatusNotifierWatcher
    [3] org.kde.*


        ID                                                          Zweig  Op Remote  Download
 1.     org.kde.KStyle.Adwaita                                      5.15   i  flathub   < 6,1 MB
 2.     org.kde.Platform.Locale                                     5.15   i  flathub < 341,3 MB (partial)
 3.     org.kde.PlatformTheme.QGnomePlatform.Sources                5.15   i  flathub < 472,7 kB
 4.     org.kde.PlatformTheme.QGnomePlatform                        5.15   i  flathub   < 4,7 MB
 5.     org.kde.PlatformTheme.QtSNI.Sources                         5.15   i  flathub  < 39,8 kB
 6.     org.kde.PlatformTheme.QtSNI                                 5.15   i  flathub   < 1,2 MB
 7.     org.kde.WaylandDecoration.QGnomePlatform-decoration         5.15   i  flathub   < 4,7 MB
 8.     org.kde.WaylandDecoration.QGnomePlatform_decoration.Sources 5.15   i  flathub < 472,7 kB
 9.     org.kde.Platform                                            5.15   i  flathub < 387,5 MB
10.     de.bund.ausweisapp.ausweisapp2                              stable i  flathub   < 7,6 MB

Proceed with these changes to the system installation? [Y/n]: n

(In reply to wurstsemmel from comment #3)
> FYI, the flatpak from flathub.org comes with more than 1.5 GB of KDE
> dependencies. For that reason I did not test the flatpak, but maybe this
> information helps with troubleshooting.

The Flatpak image works for me on the same machine with the same mobile phone.

(In reply to bvoss.srvc from comment #4)
> (In reply to wurstsemmel from comment #3)
> > FYI, the flatpak from flathub.org comes with more than 1.5 GB of KDE
> > dependencies. For that reason I did not test the flatpak, but maybe this
> > information helps with troubleshooting.
> 
> The Flatpak image works for me on the same machine with the same mobile
> phone.

For me the flatpak image works as well.

Still trouble with AusweisApp2. I tried both installations versions (rpm & flatpak).

Initial connecting works fine. Use to read the data from German ID doesn't work.

fedora 33 + Samsung Galaxy S9 (The AndroidApp can read my ID)

After flatpak install and test this is the Journal output:

Journalctl -f:
Nov 16 18:05:24 localhost.localdomain AusweisApp2[9316]: remote_... 2020.11.16 18:05:24.604 9321 C ConnectRequest::ConnectRequest(remote_device/RemoteConnectorImpl.cpp:192)  : Start reconnect to server
Nov 16 18:05:24 localhost.localdomain AusweisApp2[9316]: remote_... 2020.11.16 18:05:24.840 9321 W ConnectRequest::onError(remote_device/RemoteConnectorImpl.cpp:111)         : Connection error: QAbstractSocket::SocketError(13)

You could try to remove the custom "/usr/share/AusweisApp2/openssl.cnf" file of Fedora as it cuts down TLS stuff (why???).

(In reply to aklitzing from comment #7)
> You could try to remove the custom "/usr/share/AusweisApp2/openssl.cnf" file
> of Fedora as it cuts down TLS stuff (why???).

I tried that, but without success. I am still getting the errors:

remote_... 2021.03.14 19:40:57.540 137138 W ConnectRequest::onError(remote_device/RemoteConnectorImpl.cpp:111)         : Connection error: QAbstractSocket::SocketError(13)
remote_... 2021.03.14 19:40:58.371 137138 C ConnectRequest::ConnectRequest(remote_device/RemoteConnectorImpl.cpp:192)  : Start reconnect to server
...

This message is a reminder that Fedora 32 is nearing its end of life.
Fedora will stop maintaining and issuing updates for Fedora 32 on 2021-05-25.
It is Fedora's policy to close all bug reports from releases that are no longer
maintained. At that time this bug will be closed as EOL if it remains open with a
Fedora 'version' of '32'.

Package Maintainer: If you wish for this bug to remain open because you
plan to fix it in a currently maintained version, simply change the 'version' 
to a later Fedora version.

Thank you for reporting this issue and we are sorry that we were not 
able to fix it before Fedora 32 is end of life. If you would still like 
to see this bug fixed and are able to reproduce it against a later version 
of Fedora, you are encouraged  change the 'version' to a later Fedora 
version prior this bug is closed as described in the policy above.

Although we aim to fix as many bugs as possible during every release's 
lifetime, sometimes those efforts are overtaken by events. Often a 
more recent Fedora release includes newer upstream software that fixes 
bugs or makes them obsolete.

I cam reproduce the bug on Fedora 34 with AusweisApp2-1.20.2-11.fc34.x86_64.

The AusweisApp2 on Fedora 34 does not recognize the Smartphone as Card Reader. Pairing works, but verifying the ID Card does not work.

@besser82, please change the "version" to 34.

Fedora 32 changed to end-of-life (EOL) status on 2021-05-25. Fedora 32 is
no longer maintained, which means that it will not receive any further
security or bug fix updates. As a result we are closing this bug.

If you can reproduce this bug against a currently maintained version of
Fedora please feel free to reopen this bug against that version. If you
are unable to reopen this bug, please file a new report against the
current release. If you experience problems, please add a comment to this
bug.

Thank you for reporting this bug and we are sorry it could not be fixed.

reopened against Fedora34: https://bugzilla.redhat.com/show_bug.cgi?id=1964669

I received an update for AusweisApp2 today. Not sure whether the update was intended to address this bug.

However, the bug still reproduces with the new version:

$ rpm -q AusweisApp2
AusweisApp2-1.22.2-1.fc34.x86_64

FEDORA-2021-b025f69683 has been submitted as an update to Fedora 34. https://bodhi.fedoraproject.org/updates/FEDORA-2021-b025f69683

FEDORA-2021-5729f02f4c has been submitted as an update to Fedora 33. https://bodhi.fedoraproject.org/updates/FEDORA-2021-5729f02f4c

FEDORA-2021-ae621237b4 has been submitted as an update to Fedora 35. https://bodhi.fedoraproject.org/updates/FEDORA-2021-ae621237b4

FEDORA-2021-ae621237b4 has been pushed to the Fedora 35 testing repository.
Soon you'll be able to install the update with the following command:
`sudo dnf upgrade --enablerepo=updates-testing --advisory=FEDORA-2021-ae621237b4`
You can provide feedback for this update here: https://bodhi.fedoraproject.org/updates/FEDORA-2021-ae621237b4

See also https://fedoraproject.org/wiki/QA:Updates_Testing for more information on how to test updates.

FEDORA-2021-5729f02f4c has been pushed to the Fedora 33 testing repository.
Soon you'll be able to install the update with the following command:
`sudo dnf upgrade --enablerepo=updates-testing --advisory=FEDORA-2021-5729f02f4c`
You can provide feedback for this update here: https://bodhi.fedoraproject.org/updates/FEDORA-2021-5729f02f4c

See also https://fedoraproject.org/wiki/QA:Updates_Testing for more information on how to test updates.

FEDORA-EPEL-2021-7e4f239518 has been pushed to the Fedora EPEL 8 testing repository.

You can provide feedback for this update here: https://bodhi.fedoraproject.org/updates/FEDORA-EPEL-2021-7e4f239518

See also https://fedoraproject.org/wiki/QA:Updates_Testing for more information on how to test updates.

FEDORA-2021-b025f69683 has been pushed to the Fedora 34 testing repository.
Soon you'll be able to install the update with the following command:
`sudo dnf upgrade --enablerepo=updates-testing --advisory=FEDORA-2021-b025f69683`
You can provide feedback for this update here: https://bodhi.fedoraproject.org/updates/FEDORA-2021-b025f69683

See also https://fedoraproject.org/wiki/QA:Updates_Testing for more information on how to test updates.

FEDORA-2021-b025f69683 has been pushed to the Fedora 34 stable repository.
If problem still persists, please make note of it in this bug report.

FEDORA-EPEL-2021-7e4f239518 has been pushed to the Fedora EPEL 8 stable repository.
If problem still persists, please make note of it in this bug report.

FEDORA-2021-5729f02f4c has been pushed to the Fedora 33 stable repository.
If problem still persists, please make note of it in this bug report.

FEDORA-2021-ae621237b4 has been pushed to the Fedora 35 stable repository.
If problem still persists, please make note of it in this bug report.