time machine is ejecting my hard drive?

I'm trying to backup on my G-Mini so I can prepare to switch to a newer OS. I had some problems last tiem I tried this, but it ended up working in the end, this was about three months ago. This time, it doesn't want to work. The drive is attached by a USB.

The three tims it told me it wasn't mounted properly. Then it told me the connection was broken/disk ejected. I retsarted twice, and now I've been repeatedly getting that response. It beings to prepare, then spontanously ejects without me touching a thing.

Please let me know if someone can help. I'd really appreicate it!