Time Machine drive disappears when i reboot

When i reboot my iMac, my USB-connected external Time Machine hard drive does not remount, and it is not visible in the Disk Utility program. The only way i can get it to remount is to power-cycle the external drive. Unplugging and re-plugging the USB connection does not work. This could be a hardware issue (particularly with the USB cable), but i just wanted to check to see if anyone else is experiencing this problem.

Thoughts? Suggestions?