Greetings, and welcome to Apple Support Communities, tdoremus!
From my understanding, you’re experiencing some Bluetooth disconnects on your Mac and you must disconnect and reconnect them to resolve. I’d be happy to take a look at this with you!
You mentioned that this happens when using multiple Bluetooth devices, so I’d start by checking to see if there’s any potential interference that may be occurring. Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support can help you complete that process.
I’d also advise that you disconnect any peripherals (such as hard drives) to see if that helps. Once disconnected, reset the SMC and NVRAM using:
Additionally, if you normally connect via Wi-Fi, I’d recommend disabling that to see if it’s contributing to any interference you may be experiencing. If not, trying a different Wi-Fi network (such as a 5Ghz) would be advised.
Let me know the results, and thanks for using Apple Support Communities. Have a great day!