I one time used up all the demo-plays on 3DS: Resident Evil Revelations. I played it, until I could no longer, and after that I bought the game. I think the game came out later than the demo, so I had to play the demo so long, but I'm not sure anymore.
I don't know if it makes sense, like everybody says. I think the play-limit is not really limiting, as it is usually designed to have plenty of plays to know everything you can squeeze out of the demo. But I can't find a reason for them either.