I'd suspect it is the disk you are trying to back-up to, not back-up from, that has the problem. I may be wrong but if it was the from disk you'd have experienced other issues before now.
If it says none have been sucessful I assume it is correct and you presently have no backups. Surprised it didn't leave warning messages on the screen for you to see in the morning. That sounds a bit of a drop-off.
Run some disks checks on the disk you are trying to back up to. TRy to read the disk using a different PC maybe. Maybe try to reformat it if the tests spot nothing. If that fails to allow back-ups you could try a new drive. Or failng that suspect the back-up software.