External Hard Drive Becomes Unallocated

I recently purchased a LaCie external hard drive which contains a Maxtor
6L300R0. I Installed and formatted it (USB2 connection) with no problem and
successfully completed a backup. A few minutes later, the drive disappeared
from the MyComputer listing. Computer Management listed it as unallocated.
I reformatted it again and it was working properly for a few minutes and
the same thing happened again. I then connected it to another computer and
it is recognized and runs fine. Since it is recognized on one PC and not
another, it would seem that the computer is the problem but I have no
problem with any other USB device.

Can anyone explain why this is happening? I am planning on buying a
Firewire 800 card in the future. Would this solve the problem? Should I
return the drive and try another one? Any help would be greatly
appreciated. I am running it on Win XP Pro with all updates installed.