I manage to pair and use my Perixx keyboard (periboard-805L) on Ubuntu 22.04. In fact, I'm using it right now. However, after some time that I leave it idle, the keyboard disconnects and does not connect anymore. Hitting any key, it seems that it does try to connect again (the bluetooth icon appears once or twice in the system tray), but then it stays off. The same happens if I try to connect the keyboard via the bluetooth settings. The only way to make it connect again, which doesn't always work, is to remove the keyboard and pair it again.
I have tried to follow several suggestions, to the best of my ability, but nothing worked. Among those that I tried are:Bluetooth mouse not auto-reconnectingBluetooth mouse not auto-reconnecting to laptopBluetooth keyboard problem
If you need any detail or any analytics, please let me know (together with how to obtain those.)
Edit: I have tried playing with some other device (a phone, a table, a speaker), and I have no problem: I can pair them, momentarily disconnect and reconnect them without any issue.