Why are my Mac mini's dropping the share session now and not resuming it?

I have a 2014 Mac Mini running Mojave (10.14.6), and a 2018 Mac Mini running Catalina (10.15.7). I set up a desktop / space on the 2018 device with a screen share window to the 2014 device, and it has been running flawlessly for years. The 2014 device is basically headless, although I keep it plugged into the monitor and a USB mouse so I can fiddle with it directly when needed, which has been extremely rare.

Since I'm sure a lot of people will ask if I don't address it, I do this because I cannot upgrade the older one to newer versions of MacOS without losing access to 32-bit apps that I use periodically, but not enough to justify paying for newer versions. And I don't want to upgrade the 2018 machine because I'll lose access to other apps. (If I could suck the entire 2014 machine into a VM legally and eliminate the older hardware, I'd do that. But Apple doesn't want you to do that that.)

This approach works quite well for my needs. The point is, I have not updated either one in a very long time, and I don't plan to do so unless / until Apple stops cutting off access to older tech in newer versions of the OS, which is never going to happen. I'm looking at getting a newer Mac Mini with an M4 in it and connecting the older ones via screen share to retain access to both of them. But sooner or later, they're going to die, and I'm not sure what I'll do at that point, other than replacing the dead device with one that's working.

Anyway, I work on the 2018 machine all day long for most days, and at the end of the day I put it to sleep. The 2014 machine has always appeared to remain connected, so when I wake up the 2018 machine the next day, I can go to the same space / desktop and the 2014 machine's screen share is still alive and working. It may disconnect when the 2018 machine goes to sleep and automatically re-connects when it wakes up, or maybe it just stays alive. I don't know, and I don't really care, as long as it's maintained automatically.

Once in a while, the share session between the two fails to re-connect and I have to close the window. But I keep a Finder window open behind it, and the 2014 machine shows up in the left sidebar under Locations (Mac Mini 14) and in the Network, and I simply click it to re-establish the share link and then click "Share Screen" and it reappears.

A week or so ago, something broke for no apparent reason, and now the connection always fails to get restored when the 2018 machine wakes up. I have to close the 2014's sharing window and -- here's the problem -- the Share link to Mac Mini 14 in the sidebar disappears. It's also not showing up in the Network.

So I have to switch my monitor to connect to the 2014 machine, turn on the mouse, open System Preferences --> Sharing panel and fiddle with the Sharing options to re-establish the session. The sharing settings have not changed; I have to un-check and then re-check them (three of them) to get the Sharing to work.

Then I have to go back to the 2018 machine and go to Network, select the 2014 machine, and reconnect to it manually. It shows up again in the Finder's sidebar (and Network), and then I click on Share Screen, and it comes back.

I don't mind doing this every once in a while, but now it happens every time I put the 2018 machine to sleep and wake it up again, which is at least daily. If I just walk away from the computer, it eventually goes to sleep on its own. I don't like letting it stay awake for extended periods of time (eg., overnight) when I'm not using it.

Hardware wise, I have a gigabit switch and both machines are connected to it by CAT-6 wire as opposed to WiFi because the wired connection between the two machines is WAY FASTER than using WiFi.

The WAN port of the switch goes to my T-Mobile Home Internet modem. (Actually, the switch's WAN port connects to a WiFI bridge because plugging it directly into the modem limits the modem's download link to 92 megs, but with the WiFi bridge, it goes up to >800 megs, as reported by SpeedTest.)

Again, all of this has been working flawlessly for several years now.

The only thing I've done recently that might have had some impact is that I upgraded the T-Mo Home Internet device, but I don't know why that would have any impact, since the two Mac Minis are connecting via the switch they're both connected to by wire -- this is a point-to-point circuit that doesn't go through the modem.

What I want to address is why the Sharing session between the two Mac Minis is no longer being maintained when the 2018 machine goes to sleep and/or re-connected when it wakes up again, when nothing on the 2014 machine has changed?

This sharing session apparently has to be initiated or re-started directly from the 2014 machine, which is headless, and that's a PITA. Is there anything I can do from the 2018 machine to restart it?

Why is it dropping the Share session now and not resuming it? Is there any way to fix this?

[Re-Titled by Moderator]