back in the days when I ran the software support team at a well-known now defunct large supplier of PCs to the UK home market, we had a failure rate of wireless mice approaching 70%
Things have much improved, but still don't trust them.
In this particular case, with the Logitech wireless, I wonder if part of the problem is that the Logitech mouse software has been installed? That software is junk and only really exists to provide a back alley for Logitech to download spam adverts onto the PC. Most mice simply work when they're plugged in - they don't need the crapware that the manufacturers supply. In many cases that software cripples machines