Years ago, I read a tongue-in-cheek list of tips on how to win at chess. One of them said, "Never resign. There's always a chance that your opponent will drop dead before he can checkmate you."
In somewhat serious play and definitely professional play it would be considered bad manners to not resign a obviously lost position, and also kind of insulting to the opponent in not accepting he can win such a obvious position and making them play it over the board.