how much ram does the server have? is it possible things are falling apart after some time due to out-of-memory kill?

The ram isn't a problem it's the way the Server does things that causes issues sometimes when things get too hectic and the Server spends time on things that should take milliseconds instead taking seconds or more to complete. In the past that has including creating waaaaay too many tasks to send out and not processing the completed tasks fast enough so an imbalance appears and a reboot and the Admin doing something to cause the Server to fix the imbalance is required. It sounds like Kevin has an idea of how to fix the problem and hopefully it will be the right one.

just

just

??