Magic Mouse 2.0 cannot stay paired with different computers

I have 2 MacBook Pros, both running OS X 10.11.5 (one for work and one for home). I use the same Magic Mouse 2.0 and Apple Wireless Keyboard for both. The keyboard works great and connects to whichever laptop is turned on within a few seconds. The mouse, however, fails to connect everytime I switch laptops. Simply clicking the mouse after switching laptops does nothing. Opening the Bluebooth menu and clicking connect on the mouse will result in a popup saying "Connection unseccessful. Please pair this device again." At this point even clicking Pair from Bluetooth preferences, typically fails and power-cycling the mouse is required before it will repair.

As long as I don't switch laptops everything is fine. I can reboot the same laptop over and over with no mouse connection issues.

Log error messages (identical on both laptops):

6/6/16 10:12:01.960 PM blued[101]: Save link key for device: ab-cd-23-1e-d4-ea

6/6/16 10:12:01.966 PM blued[101]: Removed device :ab-cd-23-1e-d4-ea from the blacklist

...

6/6/16 10:12:05.935 PM blued[101]: Device Connected with address: ab-cd-23-1e-d4-ea and classOfDevice 0x002580 and connectionHandle 0x000c

...

6/6/16 10:12:06.018 PM blued[101]: Delete link key for device: ab-cd-23-1e-d4-ea

...

6/6/16 10:12:13.694 PM System Preferences[19267]: Failed to connect (mPasskeyDisplay) outlet from (IOBluetoothDevicePairViewController) to (IOBluetoothPasskeyDisplay): missing setter or instance variable

6/6/16 10:12:13.695 PM System Preferences[19267]: [BluetoothHIDDeviceController] EventServiceConnectedCallback

6/6/16 10:12:13.695 PM System Preferences[19267]: Error: [AppleBluetoothHIDDeviceGen2][_setEventService:]Couldn't copy BD_ADDR

6/6/16 10:12:13.695 PM System Preferences[19267]: [BluetoothHIDDeviceController] EventServiceDisconnectedCallback