Backing up a large sparsebundle using Time Machine I use a large (presently 16GB) sparsebundle as a container for all of my professional work.  This is convenient for me because it is an isolated, secure, "portable" entity where all of my work can be stored in one place.  It has persisted over three laptops and several hard drive changes (basically copy it from one to another as needed).  It has worked great.  In the past, I've used ChronoSync as my backup utility of choice: separate documents to backup drive excluding sparsebundle, then a second document to backup the mounted bundle as a filesystem -- thus, entire bundle is not copied every time, just changed files.  But, I have recently started using Time Machine given the wonderful integration it provides.  However, I'm not convinced it is handling this large sparsebundle properly:


I can't seem to access it via the Time Machine itself.  The only option presented is "restore".  I don't want to "try" that out.  I created a test bundled (100MB) with the same security.  I put a few files in... manual backup via TM... added a few more... manual backup... deleted a few... manual backup.  However, when I restore those via the TM interface, the changes don't seem to track.  There is indeed a backup instance for each manual backup, but the instances don't correspond to the changes made.  Perhaps I am going faster than the system is actually writing to disk? (probably 1 minute between changes).  
Directly accessing the filesystem (Backups.backupdb) shows the large 16GB sparse bundle present in most (all?... haven't checked) backup instances (e.g., 2013-02-28-042451).  The filesystem reports it as 16GB, prompts for the password if I attempt to mount it, but then fails with "no mountable file system".  I guess this is to be expected as I don't think Time Machine backups up the ENTIRE bundle each time... but I can't even mount the ORIGINAL bundle from the first backup, which I would presume is a true copy.  


The questions are: does Time Machine definitely handle large sparsebundles properly?  Should I be concerned about my testing with the small bundle?  Is there any way to access individual files within a Time Machine backup of a large sparsebundle, or does the whole bundle need to be restored?
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.