No, you won't run out of milk, hun, even if she's continually feeding. They fill as they are emptied. With an all day feeding frenzy though, you'll not get the chance to feel 'full', so to speak (if you ever do), so you might feel like you're running out, but rest assured you are not!

She will just keep stimulating until she's satisfied. It might take her a bit longer, your let down (which happens repeatedly during a bf) might be taking more time than she'd like at various stages, but you won't be empty! Also, if you are starting to get a bit stressed about it (not to mention tired) not only will that be affecting your let down, but Ava may pick up on it and it might make her a bit fussier.

Hope you're having a good break while she's sleeping. Remember to drink heaps and rest. Support your body while it notches up your supply.