I've never loved the idea of trusted X11 connections to shared machines. However, several years ago, we noticed that untrusted connections stopped working after a very short amount of time. After some digging, I found out that there's a "ForwardX11Timeout" setting that's set to a low-ish number; changing it to a big number (596h, in my case) makes the problem effectively go away.
But! I'm wondering if there's an important reason why this is set to a low number. Am I better off using a trusted X11 connection for some reason? ForwardX11Trusted (or
ssh -Y) also makes the problem stop manifesting.