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Then said Saul unto his armourbearer, Draw thy sword, and thrust me through therewith; lest these uncircumcised come and thrust me through, and abuse me. But his armourbearer would not; for he was sore afraid. Therefore Saul took a sword, and fell upon it.
Saul's ultimate demise was that he gave up. There is this idea that some people seem to have, that God predestined Saul to be doomed to failure no matter what he did... and that, if we are not careful, the same thing could happen to us. But that is not what we see in this chapter; What we do see, is that God kept giving Saul opportunities to be saved, even right up to the end. It was God's mercy that Saul was only injured (though he was seriously injured) and not killed. He still could have repented at that point. The only reason that Saul was doomed and didn't repent, was because he stubbornly kept refusing to repent, all the way to the end.
Application
No matter who around him tried to help him (like David), or refused to cooperate with him harming himself (like his armor bearer), Saul kept following the paths of sin. He fought as hard as he could against the very people who could have saved him. Driven by presumptuous fears, and addicted to self-deception, Saul sinned yet again: Saul, (though it it true that he was injured by enemies), fell ultimately, by none other than his own hand. What you really need to make sure of, is that you don't become your own worst enemy, like Saul did. Don't listen to the lies from the enemy that life is hopeless and that we are doomed. Forget about the paranoia and dread that something terrible is inevitably going to happen to you...that is not from Christ, and it will only be true if you let it become a self-fulfilling prophesy. As long as you still have breath, take every chance that you can, to turn to Christ and repent. Never give up.