Do they have to be feeding to use their abilities? Or do they only feed to recover from Hunger stress after using their abilities and failing the stress attack at the end of the scene?
On page 188-189 of Your World, under Blood Drinker and Emotional Vampire, it effectively says that you get an extra +1 against someone when you're feeding on them, and a free 'recovery period' when you kill someone from feeding. There are no other explicit constraints that I see.
Now, if you have a Feeding Dependency (YW190), then that will limit your power usage based upon how often you get to feed, and is very clearly stated in the RAW. Perhaps you could broaden your question?
They only usually need to feed if their powers are shut down due to feeding failure
Okay, so on a creature that has a Feeding Dependency you generally only need to feed in order to gain back powers or stress lost to Feeding Failure. In which case, you would follow the rules outlined under the Feeding Dependency (namely you can recover all stress and powers if you kill someone while feeding, otherwise you regain 1 refresh worth of powers when you spend a scene "feeding" usually off camera).
However, you can always compel the high concept of a vampire in order to try and make them feed.
Note that the more powers a vampire uses in a scene increases the odds that they're going to take hunger stress at the end of it. For more information about how the Hunger Stress track works, see here: What happens when a character's feeding stress track is maxed out?