I just checked Delta for November and found that they only fly JFK to SXM, non-stop, on Mondays and Wednesdays.
According to the Delta site, a non-stop is offered every day but Tuesday in November from JFK.
I plugged in random dates for Nov. 2016 and saw fares starting in the mid-$400 range and up to $900 for non-stops from JFK. Fares changed drastically depending on the day of the week with Saturday being the highest.
I called and was told only Monday and Wednesday had non-stop.
(I couldn't find it on the computer)
Of course we are booked Tuesday to Tuesday for 2 weeks.
I just checked their website and there are non-stop everyday but Tuesday (of course lol) Who was I talking to at Delta??