2025 update for everyone getting this problem: the UI to disable the freeze-on-backup is already in stable.
You can find it inside VM -> Options -> QEMU Guest Agent -> Uncheck "Freeze/thaw guest filesystems on backup for consistency"
View attachment 87655
View attachment 87654
I have not seen a problem with guests that are at least kernel 3.2. Prior to that there looks like some kind of bug where the disk never recovers. It behaves exactly like the old days when you got the CHS wrong on a disk and you could read some things but others were corrupt or you got IO errors.
Its good to have the option to not freeze if that indeed the cause.