Problems with a back up drive

I recently bought a new drive because i thought my last one was damaged.I t didnt respond anymore.At first the new one didnt respond either but i connected it to another firewire port and it worked.Then i had trouble setting two new partitions but after receiving some advice i managed to do that by running in safe mode.Today i tried to do a full back up and after about 5 hours i came back and noticed i lost connection again.The back up drive is still running though, but there are no icons on my desktop and none pertaining to it in disk utilities. This is most frustrating.What can i do?

i used super duper btw

Oddly I closed the computer down last night , reopened it and the icons appeared so i was able top do a full back up last night . I know with the last drive i was having the same problems of them appearing and disappearing until they no longer reappeared.Could this be a voltage problem?