I thank you for your help, Ascendi, but I have no idea what you're saying. I'm guessing I stand alone, because others do understand. What I got from it was that the batteries don't fit snuggly, and to shove aluminum foil... somewhere. I'm don't have a PhD in battery terminal dimensions and their terminonolgy. But I do appreciate that you helped.
David / Flashkube2... EXACTLY! After years and years with my wonderful white Magic Mouse, just today the exact same thing started happening, only I was losing connection every 20 seconds. Half the time, I'd get it back. I feared it was a Bluetooth error, or a hacker was "stealing my juice" So I got online here, read this stuff, wiggled my batteries around (for years and years, I've only used Duracel), and for the last 10 minutes, I have kept connection with Mr. Mouse and Mr. Mac. Keep your fingers crossed!
So if this problem arises again, I just stuff aluminum foil in there? (I'll be a wee bit neater than "stuff"). Speak "positive terminal" and "negative terminal" and "top of the batteries" to me, because "depth of the recess" and "vernier caliper" are Chinese to me. Does "battery recess" mean how the two batteries sit in its casing?
Maybe I just didn't have enough coffee this morning. I'm not ususally shtooo-pid. (don't go there!)