If the only pieces left on the board are the two kings and a knight, is it ever possible to force check mate? I mean, if the bare king avoids the edges and stays close to the opponent's knight, I don't see how the game can ever end. I was in this situation for more than half an hour yesterday and we were forced to draw.
No, it is not possible.
The knight simply does not cover enough space to checkmate the black king. When a position with insufficient material to checkmate occurs, a draw by insufficient material is declared.
Draw by insufficient material is declared when, and only when:
K vs K
K + N vs K
K + B vs K
Technically, a king and 2 knights versus a lone king can still result in checkmate. However, here the black king has to be dumb enough to cooperate and go into a corner and be checkmated. And so it is usually declared a draw by insufficient material.