If the switch turns back on, does also the Shelly turn back on?
The HA switch action doesn’t cause anything. So in the Shelly Web frontend the switch is always on.
If you turn it on/off via Shelly web interface, does HA react to the state?
Yes it does.
What does the history say?
Now while answering you I’ve reinstalled the integration and now I lost the history of the last days, but I’d say it looked good (the states were recognized)
Screenshot just shows the last 20 mins (as the date before is lost after reinstall)
Do you have any automations involving the Shelly?
Just a NFS tag to turn it on and off
Are you using the core integration, custom component or MQTT?
This one:

Have you tried to reset the Shelly?
Not yet, I wanted to find out the source of the error.
Have you tried to set the device up new in HA?
I’ve done it just now
Do you have unicast with HA as peer enabled in Shelly developer settings?
I haven’t changed anything in basic settings.
So to be honest I don’t even know where this setting is to find. And it worked until last week and all other shellys are still working fine.
Is there a physical switch connected?
No
Thank you for your questions and honestly I think with the reinstall of the integration it’s fine. If I test it now it works (but lets see how long).
But I’m still asking why this could happen, what could cause a HA-switch to be like a passive visual without function?
I have Fibaro and Shelly installed and I like both, but if I’m having problems it’s always a shelly. Is that simply the price for the low purchase costs (compared with fibaro)?