Thank you very much for the fast reply!
You even seem to have solved the problem just by asking for logfiles
Following your suggestion to copy the logfiles of the router and the modem I started investigating how the modem does store its logfiles and I found out that I can actually log-in to the modem. A fact the manual is completely silent about...shame on me for noticing this that late...
Browsing through the options I noticed that the modem has a DHCP server of its own that was probably assigning IP addresses in competition with my router. Disabling the DHCP server of the modem gave me a - so far - excellently stable connection from all my PCs to the internet
What confuses me a bit is that it worked for quite some time without any problems...is this internal DHCP server in the modem maybe a feature that was added/activated just recently in an automatic firmware update?
Anyway...you made my day!