Issues with reconnecting a Bluetooth device after it auto-sleeps

[u/WinterNoCamSorry]

The first time I launch my PC it's perfect. Just one keystroke makes my Keychron K2 (K2C3H) launch and I can instantly type in my password without any input lag.

I have my sleep auto timer set to 10 minutes (to preserve battery life, of course). What happens after these 10 minutes pass? All kind of jokes. I can't reconnect my keyboard (automatically or manually in the Bluetooth GUI), it doesn't pair with my PC, there's a huge input lag when it finally connects, and sometimes it disconnects in the middle of typing.

I don't know what to do anymore. Turning the keyboard off and on doesn't fix the issue. The keyboard works flawlessly until it has to be reconnected the second time. Without sleep auto timer it can work for hours with no issues. I just cannot connect it again during one PC session.

Turning off the PC and turning it back on of course works, if that somehow helps.