Helping him only works for a certain amount of time.
You can gain some points by doing the quest "Lost friend", also if you didn't took the payment for medicine when you cure him from his sickness it also makes him like you more. You can meet with him in the bar if he likes you enough, that's a start of the romance route.
Like red1979 said, at some point you can talk about hunting evening. If you make everything right there then you are going to get a heart and that unlocks the Hot Spring date.