Rav Heinemann mentioned during a shiur that there is no shalom zachar on Pesach if shabbos is the night of the seder. Although practically having one would be very difficult, why is this night halachically different from all other shabbos nights that we don't have a shalom zachar?
I thought, like Shalom in the comment, that there was no need to "guard over" the baby on Pesach Night. I have now seen ohr.edu takes a more technical angle
On the night of Passover, it is forbidden to eat anything after eating the afikomen - the piece of matzah eaten at the end of the Passover seder. Therefore, the shalom zachor, which is usually held after the Friday evening meal, is not held on this night.
(slightly edited for clarity)