I would expect Jet Blue will continue their daily service between Santo Domingo and NY. Their Airbus planes are efficient and there is plenty of airfreight to cover costs. Also many travelers who are citizens of one country and legal residents of the other (and dual citizens). There is no restriction for them. With the rest of the terminal in SDQ empty, I suspect Jet Blue is having no problems making ends meet on that route.
JetBlue does not currently fly cargo to the DR.