I would first check in the BIOS to be sure the USB settings have not changed. You could also try resetting BIOS defaults to see if it makes any difference.
While in the BIOS check the voltage readings for any anomalies.
What I'd be concerned about is the southbridge chip, which controls the USB ports. If the chip were failing you would get those sorts of problems. Some motherboards around the time of the intel P4 had grounding problems on the southbridge bus. If you are of that vintage check for dust, hair, or loose connections.
And a failing power supply can be a cause too. The motherboard logic is to cut off the circuit if there is an over-voltage draw, and if the peripherals are drawing more than the circuit can provide (while functioning normally) the logic could be cutting out.
EDIT: Also, if either USB device is shorting or over-drawing current, that will cause the circuit to cut out too.