Logitech mouse keeps disconnecting from MacBook Air

Hello luk210, 

Thank you for posting to the Apple Support Communities. 

The following troubleshooting steps are good to start with if a Bluetooth accessory is not staying connected as you would expect with your MacBook Air. 

1. Restart your Mac
2. Update macOS
3. Restart and fully charge your Bluetooth mouse 
4. Try removing the Bluetooth mouse connection in the macOS system settings, then connect your mouse again. 
5. Unpair your mouse from any other devices that are nearby, this will prevent your mouse from automatically connecting with other devices unexpectedly. 

If you continue to notice a connection issue, please follow these tips to check for and remove any sources of wireless interference. 

Have a great day!