I don't like completely no win situations, especially if I'm replaying the game.

Take Dark Souls as an example.

You're supposed to lose against the first boss. It's huge, and you have no real weapon. You're supposed to run away. This makes you feel like the underdog. Later on, you get weapons and can defeat it, so you feel like you've grown more powerful because of your previous failure.

Thing is, that doesn't work on the second playthrough. You've beaten the main boss, so having to lose to the the first one feels bad. Luckily, you CAN beat it, even with your crappy weapon. This way, you feel powerful compared to your first playthrough.