It is common for them to want to feed through a sore tummy. So they will feed feed feed, but when they get a bubble, or are full etc, and get a sore tummy, the sucking actually makes it feel better.
This of course only compounds the problem because they are adding to the problem by feeding more...

Make sure you are burping her, even BF babes often need it, so burp her after each breast (she may not actually burp, but the upright forces any air bubbles to rise to the top JIC).
She could also just be trying to stimulate your milk. If you were a bit behind the 8 ball to begin with, she may just be trying to up your flow. Remember it is dictated by her suckling how much milk you produce.

Sounds like you are doing an awesome job though! Perhaps if she repeats this cluster feeding in the wee hours pattern, offer the breast more often during the day, say every 2 hours rather than every 3.
Are you actually demand feeding her fully or are you sticking to the 3 hour thing the midwife got you on in hossie?