Sound like something is causing this on the server side. Files don't get disconnected by themselves and the fact that re-connecting them seems to fix the issue I'm left wondering what's disconnecting, if anything. If this happens every few days look in your server logs for other services that may be interacting with your Revit files and causing this. Do you have an off-line back to that locking the files? This will cause issues for users. Do you have a peer to peer syncing process running? This will also cause downstream issues for users. When is the last time to created a new central? Try the following.
1. Tell all users to get save to central and get out of Revit.
2. Back up the Central files and the Central back up folder.
3. Delete the Central Back up folder.
4. Open any local file, assuming it was STC successfully in # 1 above.
5. R > Save-As > Options > Save this file as a new Central after save. (you might have to do this step twice)
6. Have all users delete existing locals files and back-up folders.
7. Have all users create new locals from the new central.
8. Test over a few days to see what happens.
Thanks for posting.