I only experienced the problem when I replaced the Fritz AP 4040 with the Swisscom WLAN Box 2.

In my case (distance to WLAN router approx. 9m, radio quite 'hidden behind a wall, fridge placed in a narrow niche) this happens when I am also standing in an unfavourable place and additionally 'obstruct' the already limited signal. Reproducible. Moving a few centimetres helps (the radio keeps the station constant again).

What do you mean by "changing the transmission channels again and again"? What do you mean by 'channels' and 'repeatedly' (how often per minute or hour?) The router transmits in one frequency, usually 2.4GHz or 5GHz - and normally remains on the selected frequency setting.

But if the router keeps changing the transmission frequency, it is clear that the radio is no longer getting the signal and is looking for a new one.

Yes, I have also had the same thing. Occasionally, the unit hangs up and stops when the transmitter is being loaded.
For me, it has always helped to disconnect the device from the power supply and restart it.
Sometimes, however, it is also due to the quality of the channels. The problem does not occur with all stations.
Greetings and good luck