I firmly believe that things will get "better". JKR allowed Harry to look into Snape's pensive for a reason.
The state of Harry and Snape's relationship is the fualt of both of them. Neither of them can be held entirely responsible, and neither of them should be excused.
Come on people, this is a book designed to entertain! If Harry died, millions of children everywhere would be disapointed. He's our hero! JKR surely wouldn't do something like that! (...Please Jo, I know you're reading this...) On the same note, it is highly probable that we see at least a little improvement the Snape/Harry relationship.
In HBP (book 6; Half-Blood Prince) I believe that Harry will treat Snape differently.
Harry is turning 16, a stage that every male must go through. This is quite a pivotal stage. This is the stage where each subject briefly glimpses past the blindfold of immaturity, and chooses to either face the world outside like a man, or pull the wool back over his eyes, and remain a brat forever. To quote Ben Parker, "These are the years that you become the man you will be for the rest of your life. Be careful who you turn into."
Harry has come to a fork in the road. On one side of the path (the one that branches off to the side and then disapears behind some bushes), he can apologize to Snape and show respect. Where does this road lead? Harry has no idea and neither do we. It might lead to a (grudging) freindship. It might be a dead end.
The other path just plows ahead in the same direction it has been moving for the past five years. Harry knows where this path leads (Ironicly, this is the same path that James took). If Harry choses the path of arrogance, he will never patch things up with Snape and as a result he will never grow to his full moral capacity. In other words, he will be an immature jerk forever, and heck, maybe Hermione and Ron will outgrow him and no longer hang with him. His ego would sink him to the bottom of the ocean and he would become someone who is little better than Dudley or Draco.
No, Harry will at least attempt to patch things up with Snape (IMHO).