@Flop2006 and @FritzBox360 I really am not sure what could be the cause. In general I would agree on your assessment the handshake or maintaining the session with the Telegram API server is failing (as you call it “a timeout”). Latency between systems tends to be the bigger problem albeit TCP/IP was actually invented to work around this.
I can review the 3rd party code on which pimatic-telegram relies to see if there is anything I could potentially optimize to alleviate your frustration a bit. However, the server (telegram API) side we cannot influence.
Interesting that (If I understand the scenario correctly) the plugin does send out messages to mobile devices, while it is unable to poll the message queue for incoming messages. Actually two different mechanisms are used here. So it may be worth to dive in and analyze the differences. Might take me some time as I am working on other projects at the same time currently.