That soft clicking from a USB-powered drive usually means that it isn't getting enough power. The drive takes the most power when it's spinning up, and if the supply drops at that time the process will fail or be unreliable. Possible causes of this could be a faulty cable, or faulty ports on the computer or drive. Your success on Firewire bears this out. Amazingly, standard USB connectors are rated only for 1500 insertion cycles - but to be fair, portable drives weren't conceived when the USB 1.0 specification was being written. Depending on the quality of the connectors used, you may find that the gold plating will wear off the contacts quite quickly.

I suspect the USB connector on my portable drive is on the way out - I have to be very careful not to joj it while it's working. However I also know that the ports on my laptop are wearing out. The gold is almost gone. I've sorted my problems for now by plugging in via a powered hub. This puts the drive away from the work area, so I'm less likely to knock it; and it also supplies the drive power from the hub rather than the laptop, so the worn contacts are less of a problem.

Laurie's cooling trick is valid, and I've used it in the past as a last resort. However I'm not certain it applies in your case. It's really for when the drive itself is faulty, and I think you may have connection issues. The problem is that if your connection breaks while a file is being accessed, it can be corrupted, and even if the connection is fixed the file will stay broken.