Then there is definitely something wrong with your drive. If it does not spin down after 15 min. when unaffected by a system driver, I can think of no other reason. UNLESS ...
Tom, is it possible the Iomega Tools the linked manual refers to in order to change the default sleep times actually writes something to the physical drive hardware itself? I assumed the changes were written to the system driver preferences in software. Could the changes to affect the drive behavior be written to the disk driver as well, thereby stipulating power-save settings even when the disk is disconnected?
OK, I hate little problems like these that I take for granted over the years. So, not a whole answer but an answer: I downloaded and ran the latest Iomega Ware disk tools, since my 4.2.1 Disk Tools did not shed any light on the power-save settings. What I found is, without a disk inserted in the drive, a control panel under OS 9 allows you to set the spin down time between 1 minute and 30-60 minutes of last disk access (depending on drive model), with 15 minutes being the default. It is unclear to me whether it is the system driver that is being updated or some firmware or "PRAM" on the drive itself (but definitely not the disk): without powering off the drive and switching it to another Mac, I was back to the default 15 minutes which suggests the system driver is what's modified. However, Tom Lee's initial thought that the Zip cannot be made to spin indefinitely seems validated (and indeed otherwise harmful to what is essentially floppy disk media).
Based on this info, I would suggest your disconnected drive MUST spin down within a maximum of 30 to 60 minutes or it indeed has a problem.