Thank you for taking the time to post and welcome to the Bose Community.
I apologize for the trouble that you're having with your QC35 headphones not maintaining a connection with your Mac Mini - I hope we can get things resolved for you.
Firstly, have you tried clearing the Bluetooth pairing list on the headphones and re-attempting the connection? To do this, slide the Power button towards the Bluetooth icon for 10 seconds until you hear the prompt "Bluetooth device list cleared". Try to reconnect and see if that helps the situation.
It may be worth checking out these further steps directly from the Apple website, regarding similar issues to what you're experiencing.
Let me know if trying any of the steps I've listed improves things for you.
Sam F - Community Support
Thank you for coming back to us!
I'm sorry to hear that the recommended troubleshooting steps have not been able to resolve your issues.
Does your headset work correctly with other devices?
I would recommend making sure that the headset is up to date. Do do this, click the LINK HERE on a PC or Laptop and follow the on-screen instructions.
I'll be curious to know if anyone else in the Community is experiencing the same issue, please chime in here if you are!
I look forward to hearing from you!
Updated the latest version of Bose headphones. Updated Mac Mini (Catalina version 10.15.2). The problem has not been resolved.
Works great only with iPhone.
Take a look: