I agree, it seems unlikely two mice would have exactly the same problem. So, what are the other common components? This looks like an intermittent faulty connection somewhere.
USB mouse? Try it in a different USB port. Maybe the port connector has a problem.
Similar thought if it is in a PS/2 port.
What about any cable connection inside the computer case between the external port and the mobo (that is, if it's not part of the mobo)?
A driver issue seems less likely, but not impossible if other ideas don't work.