Henman was a talented player but you have to question his hunger and desire to get to the top of the game and the sacrifices that entails.
I'm not suggesting it shouldn't be questioned, but for me the answer is likely to be that he simply wasn't good enough, and no amount of hunger or desire would make up for that. Personally I don't believe Henman would have been capable of consistently winning slams no matter how much effort he put it, and he was clearly a tier below Sampras in terms of ability.