I've had this issue that has plagued me for the past couple of years that I never truly spent more than an hour trying to solve. When using a bluetooth mouse on distros like Manjaro, LMDE, and Linux Mint, I've ran into this problem where whenever I reboot my machine, I would have to repair my bluetooth mouse every single time. The only time I didn't have this issue with running Debian 10 and Windows.
I recently stumbled across a post in r/ArchLinux where someone was complaining of the exact same problem. I tried one of the recommended solutions and it surprisingly fixed my problem.
Open a terminal and launch bluetoothctl, run the commands agent on and default-agent before trust <MAC>, pair <MAC>, and connect <MAC>. The MAC address can be found by opening up your bluetooth manager and searching for the device in question. Note that I had to unpair my device from my bluetooth manager and repair it with bluetoothctl. It took a couple attempts, but was eventually successful.
After completing those steps, open up /etc/bluetooth/input.conf and add the line #UserspaceHID=true. Reboot your machine.
Viola! After rebooting my machine, my mouse automatically connects every time. I also discovered a handy new tool I can use in the terminal!
Thanks for reading. Feel free to send comments, questions, or recommendations to hey@chuck.is