It really helps when you say, preferably in the title, which of the many, many airports in the world you are talking about. Leaving it to the end is a bit confusing, and the title isn't likely to attract reasonable responses. Something like "Is the Rhodes airport open off season" would have been good. Unless you were worried about Gatwick.

And the issue isn't whether the airport is open but whether there are direct flights. Otherwise one would probably fly through Athens.