I believe we should make clear It's not exactly TIME LIMIT. Because a lot of people -like me- HATE time limit games and could miss this one based only on that.
I'll try to explain in the less broken English I'm capable of:
When you have a case, and only then, a time counter appears. IT DOESN'T COUNTDOWN just by messing around or exploring. It's more like a resource. If you talk to a witness, it decreases. If you try a plan, it decreases more. It's quite difficult to have it completely depleted in a normal play. But, you could try a case again only to try to improve your counter. And you have incentives to do that:
1) Cases are not that long anyway (aside the first one, which has not a time counter). It's not like you are repeating a tedious sequence all over again.
2) You can solve the case trying different things, that lead to different h-events.
3) They are really fun, very well designed.
This game is a rare case in which it could be playable and quite fun even without h-scenes. It's not the lazy filler of Lida's Adventures, or the well intended but terribly designed gameplay of ICSTOR games.