If you think logically, Sharptooth was in the Dark Underground. Loads of Leaf Eaters, likely Egg Stealers, and maybe even other Sharpteeth fell into there, most likely tot their death (and, if not to their death, to such injury that they likely couldn’t escape that well). T-rex was a scavenger, so eating recently killed dinosaurs was’t out the question. He could have eaten well there for quite a while and not bothered to chase after the silly kids.
However, first Littlefoot hurt his eye, by accident, with that thorn, and then Cera was whacking him, on purpose, loads of times with her horns and happened to bring him back to consciousness (though I bet the blows still hurt!).
Also, Sharptooth was later close to finding the Great Valley and wanting to get at the herds, at least according to the original script, so he likely no longer cared about the silly kids at that point, or at least not until they showed up again.