Just to not leave the problem unresolved on the list, we finally found out the reason for it.
We did an strace on one of the UDP listeners, and there we could see that Kamailio was sending out log messages, but on the wrong file descriptor. Actually, it was sending the log lines to one of our RTP proxies.
After telling Daniel about our findings, he dug a bit into rtpengine module and found some issues there.
After applying the two patches
https://github.com/kamailio/kamailio/commit/d76761bf95a5745240d655ee63241b8d... https://github.com/kamailio/kamailio/commit/0fbac693b4d3ed913b64c2d000f27a96...
to our setup, now we have logging servers again.
We were not able to reproduce the problem in our dev environment, only on the production systems. We have an array of 12 rtp engines defined in our config.
Thanks Daniel for those two quick patches!
Best Regards, Sebastian