Wow - I decided to redo my backups and start from scratch after everything was working just fine. The reason was that I moved 100G of data from my account to a shared family account. I figured my backups would be leaner and meaner! However, I ran into problems immediately, problems I seem to have "fixed" so I thought I would share.
So, brand new backup, 100Gb of data to copy, which is right. Ethernet to router, backing up to a USB drive attached to a Mac Mini. It did 300Mb and then just stopped. Estimated time went from 5 hours to 5 days. And it said "Waiting for index to be ready (101)". What the heck? Why is it indexing, there's not even a backup yet!
I stopped and restarted the thing 3 times. I deleted the "sparsebundle" some of the times, etc. Keep in mind, I had done the exact same thing on my wife's computer also running Lion the day before so I was reasonably sure it was possible to get working. So, I finally decided to delete my partial backup and reboot both my computer and the Mac Mini.
Now it's going gangbusters. The item count is dropping rapidly. It was 2M items and now it's 1.2M items, 24 GB of data copied so far, thinks it will be done in 4 hours. It's nice to see the item count moving down. If it's not AND there's no data transfer I get very nervous but that hasn't happened.
Anyway, I am not sure if this will help anybody or not. If you're remote is NOT a mac mini or some other mac but a Time Capsule, maybe you can reboot it as well! Or maybe I only had to reboot my computer and not the remote Mac Mini. Actually I suspect that is the case.
Anyway - it should not stop dead in its tracks like it did for me, and if it stops like that for you, give a reboot a try.
Cheers!