These are just some random thoughts so please forgive me if it sounds weird. Also, my usual disclaimer: I'm not an expert in anything.
Instead of leaving the external drive as just (Y: ) what would happen if you renamed it to something else? Like "Data Backup (Y: )". Drive - Rename
Another thought is perhaps one of your system files got damaged or corrupt in some way. You could try running a System File Checker scan. It will check the integrity of all protected Windows 7 system files and replace incorrect, corrupted, changed, or damaged versions with the correct versions if possible. SFC /SCANNOW Command - System File Checker
And a final thought is if you have any other removable USB devices like a flash drive, camera, scanner, etc. If the Iomega external drive is unplugged (or if it has a separate power switch that gets turned off) and another device is plugged in, it might be assigned Drive Y: because that's a known assigned drive letter that's been previously used. Then when you plug in or turn on the Iomega it may get assigned J: because for whatever the reason, it's also
a known drive letter that's been previously used. (I don't think Windows 7 or the computer will make a distinction between a HD, Flash drive, camera, etc. But I could be wrong.)
Anyway, just my two cents worth.