The Windows Event Log shows the Southernmost Feed is bickering with the Ethernet switch serving it. So today I locked it at 100Mbps on both ends which will hopefully eliminate these random drops resulting from the port bouncing. It started after a Windows Update a few months ago and nothing else I've tried seemed to cure it.
It was especially bad right after a reboot. I like to apply Windows Updates and reboot the thing weekly because...Windows, so you can see how that would be a problem.
I will keep an eye on it, but I think it should be solid from now on.