On the Fast Ferry website it says no Ferry available when I search for the last week of May and first week of June. Anyone knows if it is not running for the summer or it is just the website?

Smiths(Tortola Fast Ferry) and Road Town Fast Ferry alternate taking the Anegada route every two weeks. You didn't specify which you checked, but I assume it's the Road Town Fast Ferry because I think they are the only one's who show online availability.

Most likely it just means that Smith's is running that week. Change your dates by a week or 2 if you want to confirm the website is working as you expect.

Either way, it doesn't matter. They both leave from the same place so just show up on time and you'll be able to tell who's running.