The JCC is a nondenominational institution. Just as observant Jews are a minority within the American Jewish population, observant Jews are also a minority within the population of JCC members. The JCC should not be expected to maintain a schedule which is unsatisfactory to the majority of its members.
I think it would be wonderful if all Jews were observant. I think it would be wonderful if there were no need for the JCC to be open on Shabbat or holidays because none of its members wanted to use it at those times. However, at the same time, I recognize that I am in the minority and I do not have the right to impose my own practices on others. Furthermore, opening the JCC at these times is unlikely to cause anyone to violate the Shabbat who wouldn't have done so anyway. Finally, making a fuss and demanding that the JCC remain closed on Shabbat and holidays would antagonize non-observant Jews, exactly the opposite of what observant Jews should be trying to do if they wish to draw their less observant brethren toward greater observance.