As alluded to in the stack overflow comments, Carl de Marcken (ITA Chief Scientist) wrote some code to determine the longest possible shortest path between two

As alluded to in the stack overflow comments, Carl de Marcken (ITA Chief Scientist) wrote some code to determine the longest possible shortest path between two airports with scheduled flights. At that time (circa 2000) the answer was Wasu, New Guinea to Peawanuck, Ontario. The best you could do was something like 48 hours and involved a very large number of flights. On a bad day the best you could do was over 90 hours. Maybe somebody at Google could run the lisp function that computes that on current data and post the answer.