(24" 2009 iMac running Lion 10.7.5) I have a Seagate 1t usb hard drive (have done for about 6 months) . I have mounted the drive and set it up as my time machine backup drive. It will perform the first back up once connected fine but when the time comes for the next scheduled backup a warning is displayed saying "Could not complete backup" or something to that effect. If i eject the drive and remount or restart my mac it works fine at the next scheduled backup then continues to do what i have explained above.
I would disable Time Machine and turn it back on, reselecting the backup drive. If possible, it may be helpful to reformat the backup drive before reselecting it as well (though I hesitate to tell you to delete your only backup, even for a few hours. If you have a second external, you may copy the Time Machine backup data there temporarily for safekeeping).