How can I improve my vision for seeing forced draws when I feel that I am in a losing position? (i.e., 3 move repetition by perpetual check, 3 move repetition because the only available moves put the opponent in a losing game, stalemates [no legal moves available], 50 moves without an irreversible move, insufficient mating material, etc.)

Study tactics.

I think it is not so much as 'seeing them' as it is creating them.

First step is to become intimately familiar with a lot of endgame themes in which stalemates occur.