If you believe what is on Wikipedia, two things attributed to its downfall in the late 70's/early 80's.
1. Cheaper fish used during a shortage of Cod (they say 1970's - I am thinking it was the late 70's).
2. A buyout by Mrs. Paul's Seafood shortly thereafter which continued the trend of using cheaper ingredients of lesser quality than had previously been used.
I loved AT's in the 1970's, but by about 1979/1980, I noticed their fish was not as good, and having read the Wikipedia entry, I see why. http://en.wikipedia.org/wiki/Arthur_Treacher%27s Post Message
From that time, AT's has been bought out at least a couple more times, but trying to resurrect the once great chain has apparently not been so fruitful.