Okay. It reeeeaaaally pisses me off when people say Snape didn't try.
They had 26 biweekly lessons by the time the things stopped. It started out as weekly, but when Snape saw the Hall of Prophecy in Harry's mind, he made them biweekly.
On the very first lesson, he told Harry it was kind of like fighting the Imperius Curse -- that's not no direction, that's awesome direction. Harry has fucking fought that curse before, and he should damn well be able to figure out how to block Snape from his mind, then (unless of course fake Moody was making it easy on him in GoF, but I seriously doubt that)!
Snape tries to answer all of Harry's questions to the best of his will or ability. He traces his lip with his finger in thought. He weighs his words. He is trying. In the meantime, he gets a bit snarky, but Harry tries to piss him off by saying Voldemort, interrupting his explanations when he told Harry not to that, etc., and it literally says Harry didn't care if he was making Snape mad. Strike against Harry.
How did someone put it? Militaristic. They said Snape was acting very militaristically. I like this description. They were planning for a war, after all, weren't they? It goes without saying that he could have afforded to have started out a bit easier on him, but he did say that it was like fighting off the Imperius Curse. If Harry was too "Ooo, poor me, big bad Snapey is my teeeeaaaaaaaacher!" to search through his obviously-limited memory and put Snape's words of advice into practice, that is not Snape's fault. Not. His fault.
Snape's worry is quite apparent, if you look beneath the snarkiness and the militaristic approach. He wants Harry to win, not fail, we all know, no matter the reasons. Snape. Fucking. Cares. He wouldn't have made the lessons biweekly if he didn't! You think he wanted Harry in his rooms? Fuck. No.
Harry didn't even try at first! For weeks! Eventually, he started trying to clear his mind and couldn't, but does he ask Snape for help with that? Does he ask him to show him how it's done? No, he does not. Strike against Harry.
In the last Occlumency lesson, Snape dismisses Harry quite clearly. He then leaves to help get Montague out of the toilet. Harry should have left -- Snape clearly expected him to. Why would he not expect him to leave? It's Snape's office and Harry and Snape clearly hate each other. But Harry, in a "valiant" (read: petty) effort to find the dirt on Snape, enters the man's memories in the Pensive -- a Pensive which Snape was clear to hide in the cabinet most of the time, but felt it was better to go see to Montague than to lock up a Pensive when Harry would be leaving anyway. Harry breaks his trust completely, pissing him off quite justifiably, and he calls off the lessons -- after 26 long evenings of getting virtually nowhere. Strike against Snape? Nay! Strike against nosey little Harry! And, would you look at that! He's OUT.
The two of them are fucking imbeciles. Harry especially. So can we please stop putting all the blame for the lessons on Snape? Anyone who blames him fully for their failure has either never read the book or has an appallingly terrible memory.