It's hard to make backup to a FAT32 drive work. The same drive with JFS will be stable.
When I first got a 2TB USB drive, I partitioned it as one JFS volume. With lots of small source code files, I ran into the problem of chkdsk running out of memory, so I ended up splitting it into 3 partitions including one for Linux.
Still slow to do a chkdsk and have to be careful as the removable drives widget will try to run 2 chkdsks at once if chkdsk is needed, which I assume would take forever as the drive head would be bouncing around so much.
In emergencies, I've done fsck.jfs on the removable drive in Linux (Mint)