abruptly going off-line...

I have an all-Mac setup (really only 3 iMacs) that are all running v14.6.2452. The iMac OS is Catalina 10.15. The 2 most important iMacs used here, for some unknown reason, seem to abruptly go off line. When attempting to connect, I get the message: "Unable To Connect",  "Teamviewer not running on partner computer". I began using TeamViewer when v10 was the latest. Now I just don't know. I have checked System Preferences>>Energy Saver to make sure that nothing was checked that wasn't supposed to be. As well, TeamViewer Preferences: Easy Access is granted to both. In short, nothing was changed either before, during, or after any of the upgrades. I'm lost for a solution to this. Since there is a bit of mileage between the 2 sites, obviously keeping them both on line is very important. Suggestions? I'm thinking that, when both are online, a rarity in recent weeks, and after I end the session, that termination, somehow, causes the remote TeamViewer to go off line. I don't know, but that seems the most likely scenario. Both iMacs are on a batter backup so having the power cut off by the local utility company isn't a factor unless the power had been off for several hours. At that time, the iMac would shut itself off but would reboot itself when power was restored. Suggestions?