A glitch snuck into the release of Endless Nights wherein some installs may not save local high scores. High scores are still saved fine to the game center. If you are having problems saving high scores, here is a fix:
1) Delete Endless Nights from your device. (Hold your finger down on the icon until it giggles and then tap the X button.)
2) Remember to Keep Game Center to keep your game center high scores!
3) Re-install from the App Store. You can find it in the Purchased tab if you don’t want to search for it.
4) IMPORTANT: The first time you boot the game up, click the High Scores button from the menu. You must click High Scores before playing a game for this to work.
5) After clicking High Scores, play the game as normal. Your high score **should** save correctly.
I apologize for the bug. It should be fixed in the next update.