Using Time Machine with an Airport Extreme AirDisk
P2. "Time Machine could not complete the backup ...
sparsebundle could not be accessed. (Error 109)."
This means the sparse bundle containing your backups is corrupted.
Try repairing it, per Troubleshooting Tip #A5.
If it can’t be repaired, your only option is to connect the drive directly to your Mac and erase the partition with Disk Utility. Then reconnect it to your Airport and let Time Machine start over. You may be able to prevent this from happening again by changing the names per problem #P1.
But this is exactly the sort of thing that frequently happens when backing-up this way, and why it’s not recommended, and not supported by Apple.
Time Machine can back up to a USB drive 
connected to the new, tall Airport Extreme "ac" models (6th generation) introduced in June, 2013.
But it's not reliable and not supported by Apple on the older, flat models. They have different hardware. If there's trouble with it, you won't get much, if any, help from Apple. If you decide to take the risk, you'd be well advised to have other backups; don't depend on these 100%. See Time Machine FAQ #2 for supported Time Machine destinations.