Mouse seemed to go dead

Windows 10 Home
I got on my computer this morning and my mouse wouldn't do a thing. I use one of those small, wireless Logitech mice.
I change battery, wiped it off with alcohol and changed battery again.
I forced a shutdown, unplugged my computer and then hit the start button to drain it, plugged it back in and still nothing.
By hitting a couple of keys on keyboard I got my sign-in screen to come up so I was able to sign in. Mouse was still dead.
I unplugged the USB for the mouse and put it in a different plugin.

Just when I didn't know what else I could do the darned thing started working again. It was like it lost all contact for a while and then came back.

Does anyone have any clue what might have caused this? I'm lucky it came back this time but I'd like to be prepared it if happens again. This is actually the second time this has happened. Can't remember for sure when, but it was some months back the same thing occurred.

Yes, I am familiar with the button you refer to. However, I've been using the very small Logitech mouse which does not have this. The one I'm referring to says M 315. The one I use on my laptop is excactly the same but it says M185. I have half a dozen other Logitech mice but for me they feel too heavy and big. I bought one of these small ones for my laptop and fell in love with the weight and feel so I purchased another for my desktop. They have the tiny USB plug.

I've been using these for a long time and never had a bit of trouble until these couple of instances I've mentioned,

This information is very helpful. I have a little USB plug (receiver?) that I plug in for this mouse. The mouse itself has that "unifying" logo on it, but the USB received that came with it does not have that logo. So if I purchase one that states it is unifying and replace this one with that and then download the software ... am I understanding this right or am I way off?

It's a tab that you slide out.