Yes, Linckia are fragile, but it has absolutely nothing to do with air exposure, regardless of how many people say it. Hobbyists repeat lots of other ridiculous things to the point that they're accepted as truth. Unless they're allowed to dry out, there is no mechanism by which air hurts them.
There are 2 main reasons they are hard to keep. First is that they're sensitive to quick changes in salinity. They've already been put into at least 4 different systems by the time you go to buy them at the LFS, and most of those people don't know or care enough to acclimate them properly. The vast majority of them start to show initial signs of their decline within 2 weeks of coming in. Oddly enough though, if you collect them in the wild yourself and eliminate the long chain of custody and series of acclimations they don't die within the first 2 weeks, regardless of whether you expose them to air.
If they make it past the first month the next big killer is a lack of food. We don't know what they eat, but the best guess is that it's components of the biofilm that forms on hard surfaces. That means they need lots of surface area to graze. In smaller tanks they last about 1-1.5 years before they show signs of decline, which is about how long sea stars can go without eating. In large tanks, if they survive the initial month in good shape they usually do well for a very long time and sometimes reproduce.
These things are not impossible to keep long term. Lots of hobbyists have done it, but they tend to have 3 things in common. They start out with healthy animals, they have large, established tanks, and they acclimate them carefully.