What is important about Gilad Shalit is that he is an Israeli soldier. Leaving him in Palestinian captivity would seem like a betrayal of the trust of all Israeli soldiers.
Israel is in an area surrounded by enemies. Its armed forces are one of the major reasons for its continued existence. They have repeatedly won wars against their enemies, thus allowing Israel to continue to exist. Furthermore, essentially all Israeli citizens serve in the military at some point in their lives. This makes the IDF more a part of society than other armies in other countries.
If Israel did not try to get Shalit back, it would seem as if it did not care about the individuals in its armed forces. This would be a serious setback for Israeli morale and would reduce confidence in the country.