I do also have Logitech MX1000 Laser Mouse.
I have not experiensed any problems with it. The simplest thing is:
1. Clean the surface it's used on
2. Don't sit on your computer way to many hours at the time, (it needs rest

)
3. Reeinstall the driver and be sure to read the manual. Not sure with yours, but i have a stationary pc and there it was recommended to use the PS/2 slot.
4. Wait a bit longer if someone else has another idea.
5. Call Logitech support/head for the store you bought it (if not on internett).
Good luck