From my experience stuttering can be super unpredictable and come up in some contexts instead of others for mysterious reasons. In this case I think it could be related to the importance that you (consciously or not) attribute to the action of the person itself, maybe that creates more tension or something. It is a big favor so it's like you know you obviously need and have to thank the person, there's almost an obligation that most definitely adds more pressure and anticipation to the moment and act of speaking. Also, the social repercussions of not thanking someone for a big favor are bigger than not doing it when it's a small favor, if that makes sense, so all this may contribute to it and to how your brain reacts in that situation.