Depends on the position. There's always some tactical chances.
why play on when down a minor piece?

I suck at chess, truly, but recently won after being down -5. But as noted above ^ this was a sub-1000 match, so ...

As Hikaru said, it's not about who makes the first blunder. It's about who makes the last blunder.
If you're playing somebody close to your rating or lower, you can still pull off a win or draw if you capitalize on one of their later mistakes. Or you could even win on time if you have more time left on the clock than they do. I wouldn't resign just because I'm down a rook or bishop, unless I'm in a tournament playing multiple games per day and resigning would give me the benefit of more time to rest before the next game.
continuing to play hoping for a blunder is silly, petty and a waste of time. If they had a mode where it auto resigns when down 3 points for longer than 5 moves I would sign up in a heartbeat
How do you decide then if the loss of a piece is a "blunder" or a "planned sacrifice"?

You don't need a Blunder to recover from 3 points down. You don't even need a Mistake. Inaccuracies are enough.

Look at this game I am 2300 and on the verge of being checkmated and I won that game.
https://www.chess.com/analysis/game/live/66531152387?tab=review

continuing to play hoping for a blunder is silly, petty and a waste of time. If they had a mode where it auto resigns when down 3 points for longer than 5 moves I would sign up in a heartbeat
3 points is nothing in the 1200-1500 bracket. I had recent back to back come from behind checkmates because my opponents did not see them coming:
https://www.chess.com/game/live/65313126645
https://www.chess.com/game/live/65221203543
If I blunder a piece I feel I don't deserve the win. If my opponent gets a piece with smart tactics then he/she deserves the win. In either case, from my point of view, better to spend my time and energy on a fresh game. Just my personal viewpoint, not dismissing those who feel differently. If my opponent blunders a piece, of course I take it but find the game uninteresting after that. I'm talking 30m per side game here. perhaps I'd feel different with blitz
defending is a very good skill in chess and if you keep resigning when you are worse than you will never improve your defense
even magnus carlsen doesnt resign, he's resilient.

If I blunder a piece I feel I don't deserve the win.
If my opponent can't beat me after I blundered a piece, they don't deserve the win.
continuing to play hoping for a blunder is silly, petty and a waste of time.
*Snip*
Just my personal viewpoint, not dismissing those who feel differently.
Too late for that, I'd suppose
I should have said "silly, petty and a waste of time FOR ME". Apologies to those who took it personally.
if I play 30m and my opponent still blunder a winning position, I take it because it's their fault for not taking such a long time to see a better move. but in most of the cases maybe I'm the same as yours (resigning after down a piece for 5 moves) so its ok to feel that way, it just depends on the position where if you feel you still have a chance to exploit opponents' weaknesses (like some back rank problems or a loose piece on opponents' side), I think you should try rather than resigning even in longer time controls.
continuing to play hoping for a blunder is silly, petty and a waste of time. If they had a mode where it auto resigns when down 3 points for longer than 5 moves I would sign up in a heartbeat