Mac Mini M2 Pro loosing date & time setting

Unless I'm mistaken, yes, the Mac mini has a logic board battery to maintain certain settings when the mains are disconnected. It would be a coin cell with a limited lifespan and not "rechargeable".

The Mac is not really designed to be removed from mains power for extended periods - days/weeks/months at a time. Doing this may drain that backup battery fairly quickly and cause the problem you are experiencing.

You say you don't have an internet connection in that workspace, which is often the case, so your best option will be to at least leave the computer connected to power at all time. There's no practical reason to dc the connection since the mini uses veeeeery little power to maintain readiness when shut down.

Otherwise, you can look into having that battery replaced.

You can make a Genius Bar appointment for hardware service using this link: Contact Apple Support - Apple Support

 Call Customer Support (800) MY–APPLE (800–692–7753) or on line /getsupport.apple.com/ 

or call AppleCare Support at 1-800-APLCARE (800-275-2273) 

The M2 Pro mini has a coin-type battery on the logic board. It is not a rechargeable battery. It is actually replaceable and appears to be reasonably accessible without a complete teardown. It looks like a CR2032 in the photos I've seen, but you won't know for sure unless/until you access it.

Unless you really want to get the battery replaced, just keep the mini plugged into mains power.

If you want to do this yourself, refer to Mac mini (2023 with M2 Pro) Battery - Apple Support

Do note though, "Damage caused by repairs performed outside of Apple or the Apple

Authorized Service Provider network is not covered by Apple’s warranty

or AppleCare plans. Such damage may cause future repairs to be subject

to out-of-warranty costs or render the device ineligible for future

repairs by Apple or Apple Authorized Service Providers."

While this job doesn't appear to be very difficult (mostly involves a lot of screws) I am used to doing my own repairs because my equipment has been so old that Apple won't even look at it if I take it to a service place, namely items considered obsolete Obtaining service for your Apple product after an expired warranty - Apple Support In this situation you'd need to decide if saving a bit of money doing it yourself is worth risking Apple refusing to look at it as a result of this should you need to take it in for a more serious repair.

I don't know about new Macs but I remember with an old Mac that as long as I left it plugged in, it would boot without issue. The main problem with old Macs was if you had a bad battery it could potentially result in PRAM corruption and boot issues.

I'd have to look it up but you could probably reset the time using Terminal commands if there's no Internet access.