Time Machine - Read-only disk...

UGH! So, I 'Get Info', and unlock it, but I cannot change it to Read & Write. However... Permissions are:
uRabbit - Read & Write
staff - Read & Write
Everyone - Read-only

What the hell? uRabbit is the only user on the computer, besides Guest. And it is an Admin account. It has been five days since a successful backup has been made, because Time Machine is being crazy.

First, it was that the disk was full. Okay... So, replace the oldest backups...? UGH!

What the heck do I do when Time Machine is not replacing backups, and the backup disk magically sets itself to read-only?

Disk Verifies and Repairs OK via Disk Utility.

 

Just ejected and turned off the TM disk. Reconnected after about thirty seconds. Selected Backup Now. No errors. But, after about three minute of watching it, I let it be. I look back a couple minutes later, and it is not backing up anymore, and it says the last backup was five days ago.


UGH!