I've had a similar problem for some time that I've never been able to resolve completely. I've 2 drives in usb enclosures that I use to back up a Lenovo G560 laptop using Casper 8.0 under Windows 7. If I plug in a drive, Casper recognises it and commences a backup procedure but the drive never sppears in My Computer with drive letters. Also, when the backup id completed I can't safely eject the drive but need to shut down and then disconnect the drives. However, if I enter Computer Management and look for attached drives, Windows can see the physical drives but assigns no letters to the individual sectors. If I right click on the sectors of the drive and assign drive letters, hey presto, they are visible in My Computer.
I also have to say that the backups work faultlessly if I swap the drives into the Lenovo and boot up. But I've spoken at length to Future Systems Developments who developed Casper and despite many helpful suggestions, they've never managed to solve my issue of not being able to easily eject the drives - although the problem developed suddenly after some years without the issue
So it would be interesting to know if your drives are visible in disk msnagement and if they csn be manually assigned letters and subsequently appear as drives in My Computer?