While on Chat, a tech decided to call me. After reviewing my case, she felt that when I first booted my Mac up (brand new) and went thru Setup, I must have done something wrong. Indeed, the Setup confused me. She told me there was only one thing left to do: Shut Down completely. Hold down Option-Command-R, and Restart (keys held down). This reinstalls the entire OS again from the net. You're on the right path when you see a little globe spinning above the progress bar. I told the tech I'd call her back when it was done downloading. It downloaded finally and I was ready for Setup again. Then my power went out! I was bummed thinking I would have to do the command mentioned above again to do the OS install.
Folks, I have no clue what has just transpired, but upon the power coming back on, I decided to reboot the Mac, just to see what state it was in, LOL. I was expecting the mouse/keyboard disconnects again. As far as I was concerned the OS never reinstalled, because I never got through setup with the tech. Anyway, I've been typing this long-winded post and not once has my wireless keyboard/mouse disconnected. Obviously, the OS reinstalled again because it's asking for names and passwords wherever needed (a number of these I had already set and "remembered me"). So basically, my computer is fine now. Working smoothly....no keyboard/mouse disconnects at all. I feel this was an act of God.
So, my advice if you are having this problem: There is the possibility that you, like I, screwed something up during initial Setup. So before you go pulling your hair out, reinstall the OS from the procedure I described above and go from there. So far, so good. Wish me luck!