I couldn't get the tickets I wanted ($650 r/t TLV to JFK) through the site. It showed up as available, but after putting in all the info it told me they were no longer available. After trying different dates for about an hour I finally just called them. Got the tickets for $710 instead of $650, and I have to do some weird stuff like fill out a form they e-mailed me and fax a copy of my credit card and passport, but at least I got the tickets.
Moral of the story, if the site is being a pain, just call them.