Julian,

If you are running the backup from the scheduler service, make sure it is
running on an administrative account.
We ones had something like this too. First, backups are running fine, and
from one day to the other, a certain drive could no longer be backupped.
ADSM reported that drive D: had an invalid drive specification.
Not one error regarding authority or permissions was displayed in any log.
But it turned out to be an authority problem.
Running the Scheduler Service with an admin account did the trick.

Give it a try.