I had a similar problem before and it turned out to be my 100MB system reserved partition that had less than 50MB of space at the time that was the problem. It wasn't my external drive at all. I actually had to mount the 100MB system reserved with a drive letter to see the free space. Then, about 20 minutes later, doing nothing myself...it had more than 50MB free. I tried the backup again and it worked fine.
There are a whole slew of
related problems on the Microsoft W7 forums. It would appear that a lot of backup failures (various error codes and messages) are down to the semi-hidden 100Mb system partition being too small. You don't have to mount it or give it a letter to see it, it will show up on any disk management utility including the one built into Windows 7 Control Panel > Administrative Tools > Computer Management > Storage - Disk Management where it is called "System Reserved". Although you can't explore it from here.
I believe you
could use this utility to resize the System Partition, but I installed a third party utility (EASEUS Partition Master 6.5.2 Home Edition - free download). First shrink the other partition(s) on the same disk to give, say, 300Mb of unallocated space next to the system partition, then expand it to use all the new space.
Try your backup now.
I believe that the root of the problem is that, over time, the system accumulates more and more system restore points (or they get larger, I'm not sure which) until there is not enough spare space on the original 100Mb drive to create the shadow copy. Once this happens the backup fails with one of several error codes and messages. One other proposed solution is to delete your system restore points. This does reportedly solve the problem, but only if you also like tightrope walking in a high wind without a safety net!

.
Why MS wrote their backup utility this way eludes me

. Why, after knowing about it for over a year, haven't they issued a fix?