I try restarting MC19 server on the server (close it and restart it), and everything works OK.
How long can I expect MC19 server to sit idle and still work reliably?
Something is wrong.
MC18 (and previous versions before that) regularly runs on my server at the office for weeks straight without issue (and I only usually close it to update the build). I'm pretty sure the copy running there now has been running full-time since the last build of MC18 came out (which was quite some time ago). The only exception would be if it had scheduled patching that required a reboot (but it is "non-essential", doesn't touch our secure stuff in any way, and is behind the firewall, so it is a lower priority anyhow, so I don't know for sure how much that has happened).
The client copy of MC18 that is running the video wall in the lobby has been running
non-stop for 3 months now, I think. Maybe longer.
That's not MC19, which is new and so could be a bit less stable, but I've not seen any differences running it at home (and it isn't like they revamped much that directly impacts the server components).
One part of what you mentioned above was confusing, though...
Clients have to LoadLibrary often on startup
What, exactly, do you mean by "LoadLibrary"?