Why do skins disappear?

Legacy skins will come back for a short time every year(sometimes even multiple times),so you'll get your chance at getting this skin sooner or later.

Certain older skins were deemed by Riot to no longer be "up to par" and retired; these skins are called Legacy skins, and are no longer available for purchase; Exiled Morgana is one of these. Other skins are only available as part of an event, so that could be another reason. Most skin bundles contain a legacy skin, so Exiled Morgana might crop up in one of those eventually.

Because killed them all. :P

I believe you can get that skin through mystery gifts, but remember that it's random and very addicting.

The legacy skins retire into the "legacy vault", for whatever reason, but it's not because Riot thinks they're ugly like they did with Rusty Blitzcrank.

Keep a look out for the bundles each month. They regularly contain legacy skins that have been retired into the vault. Sometimes Riot will put them in the shop to buy on their own as well, but they don't do that as often sadly.

Good luck getting Exiled Morgana in the future!

To quote Peter Griffon's teacher:

"Because you touch yourself at night."