Tell us precisely what model TC this is, A1xxx from the base please??
Are you upgrading from a computer? What OS and what type of computer?
If you are trying to update from iOS over wireless don't.. do it over ethernet please.
iOS 8 may also be buggy on the wireless side.
The failure to backup is likely nothing whatever to do with the firmware.
Please factory reset the TC and redo the setup.
The Factory Reset universal
Unplug your TC/AE. Hold in reset. and power the TC/AE back on.. all without releasing reset and keep holding in for about 10sec. The time is not important.. it is the front LED rapid flashing that indicates you are in factory mode.
Release reset.
If it doesn’t flash rapidly you have released reset at some point and try again.
Be Gentle! Feel the switch click on. It has a positive feel.. add no more pressure after that.
TC/AE will reboot after a couple of minutes with default factory settings and will wipe out previous configurations.
No files are deleted on the hard disk.. No reset of the TC deletes files.. to do that you use erase from the airport utility.
Run through the setup and give it all names that are short, no spaces and pure alphanumeric. eg TCgenx (x=actual gen) wireless name is TCwifi.
Then reset time machine in the computer and redirect it to the newly renamed TC.
See A4 here.
http://pondini.org/TM/Troubleshooting.html
If you still have issues.. I need to know more info.
How is the TC connected into the network. How is the computer connected to it.
Please also make sure IPv6 is set to link-local only on the computer wireless or ethernet .. however you connect.
Screenshots from the airport utility of the TC setup can help loads.