Re-connect to a TimeCapsule

I have three macs backing up to a 3Tb TimeCapsule (two MBAs and a 2011 MacMini, all running up-to-date versions of Yosemite)

Everything has worked flawlessly for more than two years, but suddenly a couple of weeks ago my MacMini got stuck at 'preparing backup'. This TimeCapsule was nearly full, but I assumed that older backups would be deleted, and the two MBAs carried on backing up as expected.

I tried:

Restarting the TimeCapsule

Restarting the MacMini

Verifying the disks on the Mac mini (there were no errors or permissions problems)

All these had no effect.

I then followed http://pondini.org/TM/FAQ.html, and turned TimeMachine off on the MacMini, trashed the TimeMachine preference file, and rebooted, then reconnecting it to the TimeCapsule.)

After this, the initial backup could not be completed, as there was not enough disk space.

I could access individual backups via TimeMachine (dating back two years), but deleting each one took about 25 minutes, and so clearing space this way wasn't feasible.

Finally, I decided just to delete the relevant sparsebundle file from the TimeCapsule drive, and repeat the trashing of the preference file, and reconnect the MacMini as an entirely new backup.

The deletion (using the Finder, not a terminal command) took a while, but afterwards, the TimeMachine App showed that the TimeCapsule had a lot of free space.

However, when I set-up TImeMachine backups for the macMini again, the initial backup fails with the helpful message "The backup disk image “/Volumes/Time Capsule/jackMini.sparsebundle” could not be created (error (null))."

The Console Log gives the following:

Although a jackMini.sparsebundle file has been created on the TimeCapsule.

I am reluctant to re-initialise the whole TimeCapsule, as the backups for the two MBAs are still working fine.

Does anyone have any ideas about how I can proceed?

Many thanks,

J.