I tried tweeting AA and asking for the $71 fare difference refund. Their response was that they do have a cutoff (but didn't confirm 1 hour). Responded and asked where the T-60 cutoff is documented, so we'll see what they say. This seems like a pretty important detail for anyone who needs a last-minute fare.
Whether there is a 60 minute cutoff seems irrelevent - by your own statement, you indicated that you didnt get to airport until T-45 by which time it is documented that passengers need to be checked in