the material is not enough to give checkmate, with my pawn in the sixth and the other in the fifth

probably they are talking about this game: lichess.org/MaIgObR9/black#143

i'll post another link to the faq: lichess.org/faq#timeout

If you don't like losing on time in a position where you can't reasonably lose on the board, I recommend playing with time increment.

If, on the other hand, you enjoy games without time increment which can lead to frantic time scrambles, you will know that losing in this way is part of the game.

In the position after 59. Kxf3, black IMHO could have forced the draw easily by simply pushing the g-pawn, forcing white to capture it, then repeating it with the h-pawn.