Fresh batteries were eventually ruled out as the solution.

The system would go for days without a recurrence, then would drop the connection a dozen times in a day. I replaced the rechargeable batteries in the mouse, figuring that was the likely culprit. After a few seconds it would usually reconnect on its own, but sometimes I would need to intervene and do it manually. Everything would be fine for hours, then the Bluetooth connection would suddenly drop. Last year, I started noticing occasional issues with the Magic Mouse I use with a 2015, 13-inch MacBook Air.