There is no issue with the Bluetooth connection on my phone, but the Bluetooth connection seems unstable on my Mac.

Here are some steps you can try to solve the issue:

1. Disable the auto-sleep mode on the keyboard by holding fn(or fn1)+S+O for 4 seconds.
2. Try to pair the keyboard with your device via Bluetooth on other channels by holding fn+2/3 (fn1+W/E for K6 and K12) to see if it works.
3. Update your Mac to the latest software version.
4. Reset your Mac’s Bluetooth Module: https://www.macrumors.com/how-to/reset-mac-Bluetooth-module/
5. Check the Mac’s Wi-Fi and Bluetooth interference: https://support.apple.com/en-us/HT201542