Oops! Further digging on the internet reveals that El Al did indeed become a pubically held corporation in June 2004 (http://www.elal.co.il/ELAL/English/AboutElAl/).

It appears that "on December 23, 2004 the holdings of Knafaim-Arkia Holdings Ltd. rose to 40% of the shares issued by the airline, and on January 6, 2005, following a decision taken at a meeting of stockholders convened at Knafaim's request, most of the members of the Board of Directors were replaced. As a result, control of the airline was transferred to Knafaim."

So, indeed, the issue of Sabbath Flights is a corporate one!

And here's the "final decision" as recently as Dec 12, 2006 from a news item distributed by Reuters: "El Al says it will not fly on Sabbath, amid threats of ultra-Orthodox boycott" My source is http://www.haaretz.com/hasen/spages/799618.html.