One of the bluetooth device on macbook is greyed out and unable to connect

It appears after each sleep - wakeup cycle, my Mac cannot connect with the bluetooth mouse properly anymore. Other devices are perfectly fine. It is just the mouse which would be greyed out and unable to connect.

My only option was to forget this device, but even in that case, the reconnection is painful as it would take many attempts and hours to have it connected successful again. I also tried several methods such as rebooting the Mac, killing the bluetooth services, etc.... but nothing worked.