My laptop has used the same mouse for years, and never complained. It's a nifty little wired USB optical mouse, designed for laptops, about £5 on Ebay. I can leave it unconnected if using the laptop where there's no room for it, or plug it in later, with no problem. What IS important, as Bushfiva says, is to plug it into the same port every time.
I think you need to investigate what your machine is doing/what driver it's loading - or how much power it can provide to the USB port. There should be 500mA, which is plenty for a rodent.