I use a wireless Logitech trackball for RSI reasons. My wife uses a random dell usb mouse because she hates the trackball. We have a single Mac mini and use fast user switching to change accounts.
On both accounts, the trackball stops tracking. It'll move the cursor for a while and then stop mid-motion. The buttons still work.
On the login window, the mouse works. When I log in from there, it works for up to a minute. Then it dies again.
I had no issues with this mouse on my previous machine (linux) and the issue started immediately when I switched to this mac.
Equipment: 2014 Mac Mini running Sierra. Logitech m570 trackball. Generic dell usb other mouse.