I believe it depends on how many times you've done the stage. After you've played it at 500 P the next time it goes to 1 Diamond. As you play it more fom that Mii the diamonds it will cost go up until it is equal to the number of stars the level has.
Yes, the price does go up when you repeat a stage, but sometimes they don't even give you the option to pay 500 P, they immediately ask for Diamonds. Mitja was saying whether or not you do depends on the star ranking. From what I've observed, it certainly seems as though the higher star rankings are more likely to ask for Diamonds, but as I've demonstrated above, it's not a hard and fast rule, you can sometimes get into the higher star rankings without having to pay Diamonds.