What is the O/S?
What size back up tapes do you use?
Do you use compression when backing up?
Just using one tape to back up is not enough. You should have one tape per day, maybe another for a full back up at the end of the week and lastly one for the end of the month.
Another suggestion when you have changed anything on your computer i.e. added programs, create a new recovery disc.
Was the back up program running when the operator closed the program?