stu28: Any ideas, how to get shadow copy working again? (And how much does it matter that shadow copy is not working?)
Shadow Copy just means it makes another temporary copy before doing the backup, rather than directly copying the original file. If nothing has changed in the meantime, it doesn't matter. I make a practice of closing all running programs before doing the backup, to avoid issues like this. Otherwise, your backup can contain a mixture of files which are up to date, and some that aren't.
stu28: I am running Win XP - SP3
I think this may be part of your problem. I never found Backup on XP to be very reliable, and on Vista it was absolute rubbish. With Windows 7 it finally works the way it was supposed to from the beginning.