Q: apple mouse connection problems

Try resetting the PRAM and SMC.

Barry

PRAM (or NVRAM) is reset like this:

How to Reset NVRAM on your Mac - Apple Support

SMC is reset like this:

Resetting the System Management Controller (SMC) on your Mac - Apple Support

Neither reset will affect your data.

Barry

Is it a magic mouse 2? If so, supposedly 10.11 is required.

Magic Mouse 2 - Technical Specifications

Keyboard/Mouse – Troubleshooting Wireless

Reset an Apple Wireless Bluetooth Keyboard, Mouse or Trackpad (Troubleshooting Pairing and Other Common Problems)

Bluetooth devices become unresponsive

Bluetooth Interference Sources

Bluetooth Interference Sources (2)

If your Wi-Fi is capable of generating a 5 GHz signal, try that.

You are welcome.

WARNING!!      Be sure you have a non-bluetooth mouse handy when you do this!

My Mac mouse was losing signal frequently so I tried the recommendation while it was working.  I clicked "Turn Bluetooth Off" and then clicked "Turn Bluetooth On."  But - DUH!  - once bluetooth was off, clicking "Turn Bluetooth On" did nothing at all!

Fortunately my wife reminded me that I have a wired mouse in my odds and ends drawer - always a good idea anyway - so I was able to plug it in and turn Bluetooth back on.  But there was a moment of panic.

Now we'll see if the original problem got solved.

I tried a number of fixes from various tech support pages, including here and gave up. 

As I do not like some of the functionality of the built in touchpad, I took the wired Apple mouse from my ancient iMac. 

As soon as I plugged it into the MacBook the connection to the Magic Mouse was restored! 

(an original Magic Mouse, not the Magic Mouse 2, on a MacBook Pro Retina, mid-2012 with OS X El Capitan Version 10.11.5)