How do you even lose days off to some work emergency? If I was scheduled to be on vacation but I have to come in for some emergency, I don't lose those days, and you shouldn't either, since you never actually took those days off.
I meant that less literally. While I might still be technically out of the office, if I'm spending time worrying about an on-going problem it's not nearly as restful as if I'm blissfully ignorant.
Personally I need to be able to put everything to the side when I'm out of office.