Are you sure all is 'clean'?

Meaning that are you recording into a open track that's free and clear, and no other tracks have been used? If there's any remmnants on the track or other tracks, this might be causing your problem? If all is 'clean' - then I really don't know either?
You've tried other Zip disks I take it? Checked available space, formatted and all that?

Sounds like a weird problem indeed.