Corrupt sparsebundle files
Here's how I un-corrupted and saved my backup:
WARNING: You need lots of time to complete this exercise.
1. Purchase a 1 TB USB drive.
2. Format new 1 TB USB drive to be Mac HFS journaled, and empty, one partition.
3. Attach 1 TB USB drive to Time Capsule USB port.
4. Use AirPort Utility to archive Time Capsule to new 1 TB USB drive.
5. Attach new 1 TB USB drive to Mac.
6. Install latest version of Disk Warrior on Mac.
7. Mount sparsebundle from 1 TB USB drive on Mac. This may be difficult, because it is corrupt, and may take a long time, and may be read only. This may create an error, but nevertheless should eventually mount the virtual sparsebundle.
8. Use Disk Warrior to repair the sparsebundle. Replace the directory.
9. Erase the corrupt sparsebundle from the Time Capsule.
10. Copy the repaired sparsebundle to the Time Capsule using gigabit Ethernet.
Things should now be back to normal. Attempt a normal Time Machine backup. If it works, you can use the new 1 TB USB drive for something else, or keep it in case you need to repeat this exercise.
Disk Warrior might be able to replace the directory of the corrupt sparsebundle directly, but I found it impossible to mount the sparsebundle this way, and also, the external 1 TB drive method allows you to see whether Disk Warrior can repair the problem on a duplicate, in case something goes wrong.
It might also be possible to get Darwin's disk-check utilities, or Disk Utility, to solve the problem, but I trust Disk Warrior quite a bit. It has helped me out of a few good jams.
I wish Apple would solve these corruption issues.
MBA 1.8 SSD; MacBook Pro iCD 2.16; Mac mini G5/1.42, Mac OS X (10.5.4), Dell WFP3007 30" Display; iPhone 3G/16/W