Although T. Garth has been involved in PT boat research and writing for a long time, I have to respectfully -- but quite firmly and definitely -- disagree with him on the subject of PT 109's A-frame mast being present ("present" in the sense that it was in it's visibly raised and upright position on the boat) under JFK. The existing photographic evidence is just too strong against the mast's presence on the boat during the JFK-command era (late April-early August 1943).
The photos of the 109 -- particularly the one of the boat at speed, at sea -- under JFK are, as Garth mentioned, damaged, but not too damaged to discern that the mast is missing. The photo of the pre-JFK 109 with all the men on her deck that Dave posted was found by Gene Kirkland, another PT boat researcher and writer, and clearly shows no mast present. A photo taken by Dave Levy, the first skipper of PT 59, of several early 80' and 77' Elco PTs at Tulagi (and the 109 was among the first 80' boats at Tulagi) published in both "PT 109 - John F. Kennedy in World War II" by Robert J. Donovan and Levy's recent book "Fast Boats And Fast Times" shows none of the three 80' Elcos with masts up.
Although the little A-frame masts of the PT 103-class 80' Elco PTs both looked good and kind of "completed" the look of the boat, the masts were ultimately superfluous for any purpose other than the flying of the national colors, and possibly may have impeded the movement around the boat during combat, specifically over the dayroom canopy. In short, "they were expendable," and it isn't surprising some -- like the 109's -- were removed.
Sorry, Garth. Best evidence shows the 109 didn't have her A-frame mast up, even before JFK's command period, and certainly not during. I'm curious to know why you're so certain it was...