Ok, so just in case this might help someone else as well:

Things kept getting worse until the router would freeze up after 1-1.5 hours already.
I could resolve the problem (at least things have been stable for several days).
While updating the firmware did not help at all, a reset to factory defaults (labeled
“revert firmware” in the menu) seemed to help. I would have expected the update of
the firmware to already fix possible problems there, but reverting seems to do something
additional.