Another reason they could be bringing up the past favours they have done for you is they could be feeling upset and as though there is an imbalance in your relationship. Similar to the transaction view, just in a more personal manner.
When thinking back to things such as past favours people tend to remember the things they did more than what others have done so whether or not it is justified, it seems your friend is upset and believes you are not pulling your weight in terms of your friendship and are trying to convey this to you by means of listing examples (not the best approach but its what they did). To respond to this you need to show your friend how you have noticed and appreciated the effort they put in to your friendship and replying with what you have done for them (that they think of as not much) did not help at all.
You need to try and empathise with her, and look from her perspective where after happily doing you a few favours, they ask for one (as you described) small favour and you reject it. Was the place you needed to be so important that you couldn't shuffle things around to fit in with the small favour? If not did you properly explain how unusually constricting this thing you need to do is and how you intend to make it up to them? Keep in mind that as you said, there is a chance they may have gone out of their way in some of their favours for you before, postponing or squeezing it in to work with the things they were doing themselves.
Simply telling your friend
I was really thankful when you did {example favour} for me, it helped a lot and I know you had other plans that day
could potentially resolve the whole conflict on the spot. As I can tell from personal experiences with a close friend who I thought was taking my help for granted and not reciprocating it. Merely being told that your effort was noticed can go a very long way.
Saying these things in a casual conversation would greatly help avoid conflict and reach a happy resolution for each of you, if you instead replied by comparing what you have done for them, or implying they have not done that much then this can lead to an argument. Even at this point, there is not much difference for how you should respond as opposed to when in the casual conversation. If you keep a casual tone and volume then saying the same things would help defuse the tension and reach a solution. I understand there is also a chance that your friend is seeing things from a biased perspective and you may have been doing more than enough already however, insisting/arguing this point in your scenario will lead to nowhere