wow - that's great play. I agree you were right not to resign.
Why not resign!
Your opponent mad a lot of blunders. Good counter-attack! I like the Rook-invasion down the b-file. And you're right, never give up!

Actually you were totally lost :) ... whether you choose to resign or not is up to you but don't ignore the objective perspective.

You never know if your opponent might just get overconfident and repeat a blunder similar to the one you made. It happened to me once, I was short on time and thought I had the game in the bag,(up a whole queen) so I acted rashly. Let's just say it was the worst loss I have yet to endure in a game of chess, simply because I know I should've won it ten times over. Bah :(
Why not resign!
I am a bad player, I know. I'm learning.
I put much effort and... I am very stubborn. When the opponent is the same level of my I fight to the end.
Here an example.