Backing up crashes Leopard!

Since installing and updating Leopard to 10.5.1 on my G4 Mac mini, I have been unable to backup my system since any attempt to do so crashes OS X altogether. I am using a partitioned 500 GB SimpleTech USB external hard drive, partitioned into 2 equal partitions, one for this Mac mini and one for my G4 iBook (though I don't use it for the iBook anymore since getting a separate firewire ext HD for the iBook, which works well for backups). Previously with 10.4, I was able to back up the Mac mini system using the SuperDuper backup software program. Now, with Leopard installed, the Mac mini system backs up a little over half way and then OS X 10.5.1 Leopard crashes completely. This happens whether I use Time Machine or SuperDuper, and has happened repeatedly. I have repeatedly reported the crash to Apple when the screen presents the option, but have of course received no solution and therefore cannot backup my G4 Mac mini. As Time Machine backs up the first halfway or so, it indicates that I have plenty of available space on the external HD and I emphasize that backups were ALWAYS successful with OS 10.4 Tiger. Is the problem my external HD and would it help to try to erase it completely and remove the partition, since it isn't used anymore for the iBook? I find it strange to think that the external HD could repeatedly crash the Mac mini's OS X Leopard during back ups, but I'd be willing to erase it if that would help.
I would be VERY grateful for any help. Thank you.