My take on this is that the search goes on for two major reasons.
First, we human beings (at least modern ones) seem to love a mystery. We aren't very good at just letting go of anything.
Second, and perhaps more importantly, this particular mystery has a very exciting setting. We have the relatively early years of aviation when flying was an adventure. We have the fact that Earhart was a female pioneer in a male-dominated area. We have the looming specter of World War II and the possibility that Earhart was caught up in that impending conflict. Then we have the exotic locales in the "South Seas." It seems to me that all of this makes for a particularly enticing mystery.