I updated VLC now (server and client side), but the Results are the same. I also tried other web stream players (AIMP 3, MTA:SA, WMP) and all have the same issue so I guess it's a serverside issue.
The log of the Server does not shows much Information (VLC was started with --verbose=2). Below is a screenshot of the actual situation. At this Point the Server was running for half an hour and a client was listening for 15 minutes.
I also find it interesting. that in the Output Part of the Statistics Dialog, everything is zero. And for some reason the Log Dialog is empty while the Console shows Log messages
The Client side VLC shows this Message, when it "resets" the stream:
[006386f8] main input error: ES_OUT_SET_(GROUP_)PCR is called too late (pts_delay increased to 1000 ms)
[006386f8] main input error: ES_OUT_RESET_PCR called
VLC starts to stutter a bit, it gets worse over time and at some point it seems to pause the stream output completely to refill its buffer.