I just got a new Lacie NAS with their NAS OS 4. After making an initial Time Machine backup to this device I wanted to mount the resulting (encrypted) disk image but when doing so I just received an error message "Resource temporarily unavailable". Googling this error message returned a lot of Voodoo fixes. However, after playing around a bit, restarting a few times etc I realised that I had something called Time Machine service enabled for this share. Turning this service off immediately made the disk image available as expected.
Disable "Time Machine service" for the share the disk image is stored on.
(Note to Moderators: this answer might have to be moved elsewhere).
Let me share my experience with backing up and restoring a MBP for a family member after a wipe in preparation for a "Genius Bar" visit....
Personally, I do not use TM, but my mother does... We are both Mac users, the difference being she knows nothing about computers yet due to her stubbornness, I was essentially compelled to fix her legacy backup procedures. She uses a WDMyCloud to backup both an MBP and an iMac over her network. Being the great son that I am, I had to make sure these were running smoothly.
I struggled greatly for an entire day to figure out how the heck TM works. What a disaster. I prefer CCC, as I don't need snapshots of my system every minute. Utter ridiculousness. I can attest to there being curious permissions issues with sparsebundles, which I adjusted accordingly (read, "nuked)", but am not even sure if that fixed anything. I'll say that you must be extremely patient if you're wanting to mount said bundle in order to explore it's contents. You can't have multiple systems contending for access to your TM backups, or else you'll get the dreaded "resource temporarily unavailable". Basically, the mouse sucks and I use Cmd+O to mount any disk images, and then I WAIT SEVERAL MINUTES. It was upon this realization, and the fact that multiple machines cannot access the same disk image simultaneously, that I was able to consistently mount and explore the TM backups.
Mounting and exploring these disk images truly is a long process and requires a lot of patience. I also recommend adding all the mounted disk images to Spotlight's list of excluded locations. This just wreaks all kinds of havoc.
TL;DR - make sure only one machine is attempting to mount the sparsebundle, be PATIENT after attempting to mount (several minutes), wait another several minutes for file indexing. You might even hear your fans spool up as DiskImageMounter goes into overdrive. Add these images to Spotlight's excluded list.