Personally, I prefer the latter and I must admit that I have used that form as an abbreviation in many of the free text notes I have added to catalog records without giving it too much thought. Contemporary usage (certainly among boosters of the fair) appears to come down slightly in favor of “AYP,” although there are plenty of examples of “AYPE” as well (as below).
I recently was reminded of the issue, however, when I was having another look at how one of “my” records was displaying in UW WorldCat (yes, this is what I do in my downtime) and was truly startled to see that one user (jcputman) actually had added that item to a list he or she had created and named “ayp.” I was especially curious because this was the first time I had ever seen any of the “social” features in WorldCat (which include lists, tagging, and reviews) implemented. I searched the lists again and found that another user (kmrcnw) had created a (slightly longer) list called “aype.” Maybe the two of them will want to compare notes now (or maybe not). But what I also found intriguing during the search process was the discovery of yet another list, “NCLB and AYP,” which clearly had nothing at all to do with the Alaska Yukon Pacific Exposition. I was able to figure out from the items listed that “NCLB” referred to the No Child Left Behind Act, but it took a Google search to discover that “AYP” here meant “Adequate Yearly Progress.” Just further proof that context is everything in description and that controlled vocabularies can be useful?