They are primarily saved locally. If you have made a level you're satisfied with you can choose to upload it. If your level isn't played for a while it will be removed from the server, but not from your game.FoolKiller said:
OT: I can assure you this has happened to everyone who has ever played Super Mario Maker. While it's a shame that good levels will be removed eventually this is to get rid of the levels no-one wants to play. I don't know how his levels looked like, but I am assuming they were hard and kinda unfair meaning you'd have to know what to do in order to complete them I can see why they wouldn't get mainstream popularity. I have seen fairly moderately challenging levels remain uncompleted. Whenever I encounter one of these kinds of levels I skip it. It may look like fun on a Youtube run, but it's dreadful to play.
If you really think Nintendo should maintain server cost for something which appeals to maybe 5% of their audience why shouldn't they also keep all those levels where you just run in a straight line for a minute then beat it. Those also remain unplayed until they get removed. I really think Nintendo should just tell him to stop being an entitled ****. He's popular on Youtube, but not on Super Mario Maker. There's no conspiracy, this is how the game works.