I had this exact same problem, which is why/how I found this page. Bloody annoying as F, especially since this appears to be the only place in the web-verse addressing the issue.

I appear to have solved my problem, and perhaps yours as well.

  After going through troubleshooting steps, here's I what have working now:

• I commended out AutoConnectTimeout in /etc/bluetooth/main.conf -- not set to 0, but commented it out completely. Not sure if this matters, but I'm keeping it that way for now. I don't want AutoConnectTimeout to time out.
• I set my IdleTimeout in input.conf to 240 minutes; this is a computer dedicated to watching movies, so... yea, can't hurt.
• I set "RememberPowered" in main.conf to "false".

I was really wracking my brain on this, fearing I would ultimately have to write an F-ing script to ping my mouse via Bluetooth. However, after trying out different combinations of settings in the input.conf and main.conf files... my eyes rested on the "RememberPowered" option in main.conf... it was set to "true". Wait, I want my computer to remember that my mouse was powered off? F no -- I don't want my computer to remember any power-state of any mouse; just go connect and keep powered and keep connected and keep talking, and I don't care if the mouse isn't listening because I turned it off. So I set that to "false". It appears this has solved my problem of my Bluetooth mouse not re-syncing up and re-connecting to input services after a long time of being turned off, with the computer still on.

I hope this helps you.

Note: It doesn't matter if you have USB mice or USB keyboards connected to your computer.

I appear to have solved my problem, and perhaps yours as well. After going through troubleshooting steps, here's I what have working now:

• I commented out AutoConnectTimeout in /etc/bluetooth/main.conf -- not set to 0, but commented it out completely. Not sure if this matters, but I'm keeping it that way for now. I don't want AutoConnectTimeout to time out.
• I set my IdleTimeout in input.conf to 240 minutes, this is a computer dedicated to watching movies, so can't hurt.
• I set RememberPowered in main.conf to false.

I was really wracking my brain on this, fearing I would ultimately have to write an F-ing script to ping my mouse via Bluetooth. However, after trying out different combinations of settings in the input.conf and main.conf files. My eyes rested on the RememberPowered option in main.conf. It was set to true. Wait, I want my computer to remember that my mouse was powered off? I don't want my computer to remember any power-state of any mouse. Just go connect and keep powered and keep connected and keep talking, and I don't care if the mouse isn't listening because I turned it off. So I set that to false. It appears this has solved my problem of my Bluetooth mouse not re-syncing up and re-connecting to input services after a long time of being turned off, with the computer still on.

I hope this helps you.

Note: It doesn't matter if you have USB mice or USB keyboards connected to your computer.