Time Machine couldn't complete the backup to "Time Capsule. The backup disk image /Volumes/Data/MacBook Pro.sparsebundle could not be created (error 60)"

Question

We are Mountain Lion using Time Machine to backup to Time Capsule. When the backup tries to run, an error appears after a couple of minutes saying "The disk you inserted was not readable by this computer." Then an error shows up saying "Time Machine couldn't complete the backup to "Time Capsule.The backup disk image /Volumes/Data/MacBook Pro.sparsebundle could not be created (error 60)"
I low level reformatted the Time Capsule and that didn't fix it. I then tried using Time Machine on another computer to back up to that same Time Capsule and it worked- so I'm doubting it's the Time Capsule.
I've noticed that when Time Machine runs, that a  folder called Data  at /Volumes/ appears while Time Machine is trying to back up. I think it's making the sparsebundle to transfer to the Time Capsule.
However, after a couple of minutes- it comes back saying that the disk is unreadable.
I think it's something wrong with either creating the sparsebundle or opening the disk image that seems to be a part of the Time Machine backup process on the local drive. 
I am able to create a disk image with Disk Utilitiy without any problem on that system. I've repaired the disk and disk permissions with Disk Utility and replaced the directory with Disk Warrior. I've trashed what preference files I could find and restarted. I've completely removed the backup destination from the computer and added it back again.
Help!
Thanks,
Neil

Answer 1

neillhowell wrote:
I've noticed that when Time Machine runs, that a  folder called Data  at /Volumes/ appears while Time Machine is trying to back up. I think it's making the sparsebundle to transfer to the Time Capsule.
Yes, exactly.  It makes one sparse bundle per Mac.
It's possible the TC's disk is too full for a new sparse bundle, or there may be some other problem.
Via the Finder, locate the existing sparse bundle (see the pink box in Time Machine - Frequently Asked Question #17 if you're not sure how to do that).  See how large it is (plus how large anything else that may be there).  If the total is very near the size of the TC, that may be the problem.
If not, a clue may be lurking in your logs.  Use the widget in #A1 of Time Machine - Troubleshooting to display the backup messages from your logs.  Locate the backup in question (probably the first one displayed), then copy and post all the messages here.