This happened to me. My wife has a SONY PC and, I'm reasonably sure, a Logitech wireless mouse that started behaving strangely, like you describe. The OS "picked up" the mouse for a short while, but it droped out entirely. Did all the usual, changed the batteries, tested on a different PC (that presented another set of problems however), etc.
I did do some research into it, and found some resources like
Microsoft KB321122 article. The thing is is that 99% of what you find when doing searches like this is the same moron repeating the same moronic advice (eg replace the batteries) which overshadows any useful information. Worse, when I was writing this post, I tried to find the corresponding Logitech article and found
this crazy ---steaming pile of meadow muffin---....
But back to the topic, In those two links above are software package that might include the 32-bit drivers you need. It's worth a shot. I never really solved my mouse problem. My wife ended up buying a new wireless Logitech mouse and it became a non-issue and the old mouse became a donor in my parts bin. Might as well save yourself the hassle and get a new mouse. Short of intense gaming or top-of-the-line tech, these wireless mouse are all basically the same.