It might help to list the rest of your system specs, and also what kind of Zip drive (ATAPI internal? SCSI external???) that you're using...
I once had major problems trying to get my ATAPI Zip working on the same channel as my old HP 8110i CD-RW drive - some weird hardware conflict. Moving them to different IDE channels (i.e., one on the primary, one on the secondary) fixed my problems. Maybe try isolating your Zip drive on its own channel? (Assuming you're using an IDE one... like I said, give us some specs)...