I spent a month on the phone with 2nd level Tech support and engineering - every other day.
I have 4 computers (one was a clients), all with different backup systems: Time Capsule over CAT 6 Gigabit Ethernet through a Thunderbolt monitor, internal eSata to external 6 TB RAID 5, Wireless to Time Capsule, Firewire 800 to External 2 TB RAID 1 dive.
With the install of 10.8.5 (the itermediate update to 10.9) I immedialety had Time Machine problems on all four computers. As I said, I spent a month talking with Apple. Also during this time I purchased 2 new MacBook Pro 13 Retinas. Installed Norton Internet Security 5 on them and they had the same problem. The new Retina's had 10.9 on them, so this is about 10.8.5 and 10.9.
After doing Data Capture on 3 of the computers for engineering (a new MBPro13R and my MacPro), engineering finally figured out what was happening.
Norton Internet Sucrity 5 for Mac is not longer compatible. As my 2nd level tech said: " Engineering said, they need to call Norton and figure out what they did to their program to cause this."
The fix is to completely remove Norton and all it's components (using the uninstall app inside the Symantec folder). Once you do that, Erase your backup drive, Restart everything, Re-connect your computer to your drive - then it immediately works perfectly.
Do Not Re-Install Norton.
I have now done this exact operatinon on 7 different machines. Time Machine works instantly. Time Machine is not the same program from 10.8 - it has been completely rebuilt, so I doesn't backup in the same way. But it works perfectly on all my computers now.
I'm not going to put Norton back in my computers until I find that Norton has acknowledged this problem, or they come out with Norton Internet Security 6.
Hope this helps