Research undertaken by the organization over the past few years suggests that the vast majority will never reapply for the popular tour, he said.
Mark, who has been involved in facilitating the trips to Israel since the initiative was launched 10 years ago, said this was "the source of much frustration.
"We don't deal with it and we don't know how to deal with it," he said. The only way was to try to increase funding, he added.
"If we had more money today we could bring up to 50,000 people to Israel a year," Mark said. "Israel is capable of absorbing many more people and we have shown time and again that we can cope with such a large number. There are no limitations on our ability to recruit more people."
He pointed out that last year, for Israel's 60th anniversary, the organization brought some 40,000 young Jews to Israel. This past summer, however, the it brought only a quarter of that number and this winter trips will see 8,000 young people arriving here.
Figures from birthright for this year show that it has raised close to $80 million for the free trips, with 55% coming from individual Jewish philanthropists, including the Las Vegas-based Adelson Family Foundation; 22% from Jewish communities worldwide and the Jewish Agency for Israel; and 23% from the Israeli government.
"Our biggest challenge today is increasing that funding so less people will be left off the trips," said Mark, adding that the organization has already started to intensify fund-raising efforts through the Birthright-Israel Foundation.
However, Avraham Infeld, senior consultant at the NADAV Fund for strengthening Jewish peoplehood and fostering Jewish continuity and a former president of Hillel and the Chais Family Foundation, told the Post that until such funding was found, a united effort was needed to keep those turned away from birthright trips from falling through the cracks.
"Having the names and addresses of these young people is an invaluable resource," said Infeld, who will speak on Jewish peoplehood later this week at the president's Facing Tomorrow Conference that opens in Jerusalem on Tuesday.
"These are the people that the Jewish world was trying to reach in the past and while, in many ways, birthright has made that possible, the main problem is the disunity in the Jewish world.
"All organizers worry about are their own activities and not about the general good of the entire community," Infeld continued. "There is a whole world of Jewish organizations that could make use of these people. If they can't go on birthright due to funding then we all need to think together what can be done for them."
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