Please mention the model # of the system.

 

A mouse driver update may fix this issue.

Does the mouse freeze after coming out of hibernation, or just doesn't work at all when you try to bring it out of hiberation?

If it just won't work, as opposed to working and then freezing, you might try this:

Open Device Manager and expand list under USB
Double-click on each USB root hub, one at a time
Click Power Management tab
Uncheck the box "Allow PC to turn of this device..."
Click ok back to Device Manager main screen and repeat for all USB root hubs.
Reboot.

Ron