I have an old Seagate portable USB drive that has started oscillating on and off in rapid succession whenever it is plugged in. The drive is very briefly (split-second) recognised, then it disconnects, then it connects again, over and over and over. 

I pulled the drive from the enclosure and put it in another one and it works fine, so the problem is obviously with the enclosure. My question: Is this a known issue and is it fixable? Why is it doing this?

Edited to add: I just put a different drive, probably one that requires less power, into the Seagate enclosure and it seems to work fine. This suggests that the issue is a power one, yet the Seagate enclosure has worked fine on different devices for years. What would cause this change?