Magic Mouse 2 Only Connects When Plugged In
It may be an issue with one of the bluetooth radios.

Can your MBP connect to other BT devices?
 - If not, you may need to get your MBP to Apple Service.

Can you connect the MM2 to a different computer via BT?
 - If not, you may need to get your MM2 to Apple Service.

If you can't test this yourself, you should get both units to an Apple store and let them diagnose it for you.  They are usually pretty good at root-causing such issues.