The Big Stretch

The Longest-Running Series, By Number of Novels
(not including short stories, collections or omnibus editions)

According to all the evidence I could gather, the Larry Kent series by "Larry Kent," a house name, is the longest-running P.I. series of all-time, while Le Manchot by Pierre Saurel, assuming he actually wrote them all, is the longest-running series by a single author. Chritopher Bush's Ludovic Travers series comes close, although Ludovic is not working as a private detective in all of the books.