As we are on island for two weeks during this time, we have always emailed restaurants under consideration if they are going to be open,
although the closings seem to be in line with previous years before Irma.
I do know that Spiga and Astrolabe will both be closed for holiday while I believe Le Cottage will be opening September 1.
Most restaurants on the Dutch side remain open.
La Villa does not close but Florence usually takes her holiday in late August, early September.