Welcome to Tom's Hardware, @gmhughes53!
It sounds like the external HDD could be defective. However, I'd definitely recommend some further troubleshooting first. I'd advise you to swap the USB cable that is connecting the external to your computer and also try plugging it to another USB port. If you have access to another PC/laptop, try connecting the drive there as well to see how it would get recognized. If you manage to keep it connected for a longer period of time, check
Disk management in Windows as well as Device Manager to see if the HDD could be seen there. Posting some screenshot would be really helpful!
ONLY if the HDD is out of warranty, you could also try connecting it internally via SATA by taking out of...