Health warning - I experiment a lot so this may not work for you!
In summary, the problem was that I have a time capsule with 2Tb of space that seemed to work fine. It had a number of flies and folders and two sparse bundles. One of the bundles, refused to mount i.e. double click would not put the image on my desktop and open in finder. I could right click and choose "show package contents" and see the "bands" directory, but it was useless in this form. Because it wouldn't mount, no software data recovery programs would work because they didn't "see" the image. The other bundle would mount and display all the backup folders. Other people here helped in suggesting tips but most felt the drive was bad or that the file was too corrupted. I tried all the things you probably have in trying to get the terminal command hdiutil to work, but it always failed with something like "Unrecognized filesystem".
In desperation, I attached to the TC from a Win7 64bit system and found something curious. You can see from the screen shots above that Windows showed each bundle as a folder with files in it. OS X didn't seem to show these to me before. I opened the files with notepad in Win7 to see what was inside and they seemed to describe the bundle in some way, i.e. included the bundle name and other info. The bad bundle did not have these info or .plist files, showing only a zero byte file and LSOverride which I deduced was some means for telling OS X how to deal with this unknown file. I copied these two band bundle files to another location leaving only the "bands" directory then copied the files from the good bundle over to the bad bundle, excluding the "bands" directory from the good bundle. Basically, I copied the "helper" files from the good bundle to the bad bundle. I don't know how one does this in OS X, so I had to use Win7 to do that. after that, I went to my OS X machine and double clicked on the previously bad bundle only to find it worked just as well as the other bundle. In fact, I found the file from 7 years ago that I was looking for and celebrated with a tall martini afterwards.
I don't know that this will help you, but good luck.
ed