I too have that Problem, It started with one of the last Updates I guess. I can’t say when, as I didn’t notice it at first and blamed my Zigbee Setup for Automations not firing /not firing exactly. A Week ago I wanted to edit them, to see what I could simplify, but I got the same behavior from HA as it is described here in the Thread:
Timeout after a few Minutes using the Web-UI or App. Access is only possible right after a restart.
Since I used an USB-SSD as my Main-Drive on a Raspberry Pi 3B, I thought it may be the culprit. It ran the last 3 years in that constellation, without any non-resolvable or understandable errors. So I changed the Drive to a fresh SSD in a new USB-Case with Trim support.
I installed fresh, on a new drive, without importing any Backups, and the Problem still persists. I Replaced The Network Cable, Changed the Network-Switch the Pi is connected to, Replaced the PSU with a rather powerfull one (5V 6A), and by now I was about to replace my Raspberry Pi 3B with new Hardware (Somehting NUC-Like), when I found this thread…
Well, I hope we can find a solution, If all our Problems maybe have the same root… I will now roll back Home Assistant Versions and see if that changes anything.