I'm partly through a discussion. with AppleCare - so they know. I've told then they have a major systemic problem.
I Have had several probs. My config is mavericks iMac -> Ethernet > Lion iMac > thunderbolt seagate drive.
First problem was fixed; I had my firewall on - fine with Lion to Lion but NOT with a mixed OS network = Terrific.
Then TM worked very slowly, then it didn't. Error was in failing to backup and create the new .sparsebundle I called AppleCare and they said they would NOT support my config, I.e. networked 3rd party drive, but they would support if I moved the Thunderbolt drive to the Mavericks iMac (but only on this iMac). Ugh!!!
So I've moved it across, and now TM works (at about 30-40mb/sec). Also my Lion iMac TM works back the other way, although very slowly. When switching the drive like this both backups seemed to be forced back to initial full not incremental on the first backup.... not what one would expect.
Anyway I'm following up with an AppleCare supervisor next week.
Having lost so much time I've also ordered a 3TB Time Capsule, so perhaps Apple got what they want - notwithstanding one more ****** off customer.
Anything new I'll post.