Backing up a large sparsebundle using Time Machine
The only time I've seen the error you report was when I stored a sparse disk bunds inside another sparse disk bundle and both were remotely mounted on a fairly slow network storage device such as a Time Capsule.

In those cases, I've often excluded the original image directory from the Time Machine backups, since it works in theory (and most of the time in practice), you can't get any benefits of browsing those files on a Time Machine backup.

I usually set up rsync or another incremental backup tool to copy those files on a schedule I like (perhaps automating it all with Lingon 3).

By restoring the file to a local drive, you'll know if the failure to mount is due to an actual corruption or just network indirection and time out.

Once it's copied to an attached or internal disk, you might also be able to use Disk Utility to patch up filesystem errors although with encrypted sparse disk bundles, that is often not successful.