wow, do I have a completely different opinion of what happened there. The Sherrif didn't miss his chance. He knew his chance was in there and he passed it up "to live another day" because he knew that if he confronted Chigur, he was a dead man. Then, in the ultimate twist of irony, as he lived his other days, he basically wished he was dead anyway, as his dreams foretold, shivering in the storm (which is what society had become) just waiting to get to other side to be with his father (or waiting to die to get to heaven).
if the Sherrif made any move toward the vent, he was dead and he knew it. As for my reasoning in how the Sherriff knew he was still in the room? He walks into the bathroom and the Coen's made a point of him recognizing that the bathroom window latch was closed, meaning there was no way he could have escaped out the back (because who would have latched the window in that case? trust me, there's a reason for every shot in that scene) He also knew that Chigur wouldn't have left the vent sitting there on the ground afterward to raise eyebrows, which meant he hadn't finished in the room yet.
The Sherrif knew he was in there and he was facing his own mortality with whatever decision he made. Face death and keep your pride or swallow it and live another day? He decided to live another day and then regretted it the rest of his life. Basically screwed if you do and screwed if you don't. Like his Uncle said, "You can't stop what's coming." Love that movie. Damn it was bleak.