I did count the War of Independence. There's this guy:
http://www.historyguy.com/arab_israeli_wars.html
...who is as generous as I was with the definition of "war"...
BUT, the original point remains. Before Nixon, the US didn't really have much concern with Israel; they were a minor matter to us. During that time, they fought and won major conflicts with major military hardware against a good sector of the Arab world, and they kicked ass and took names.
It's my understanding that the Arab world makes really crappy militaries, partly because their culture requires them to get clearance from the very top of their command chain for every little decision. (Thus, perhaps, the failure of the Iraqis to blow up the mined bridges this time around: once their communications was cut on day one, the grunts had no way to get the order to blow up the bridges, and would not take the initiative to do it on their own.)