There are two types of people in Arena

I only surrender when I bring the wrong team. Taking my under-leveled Training Tower team into the Arena because I spaced out on what I was doing.

but the moment you lose someone your score is ruined and won't reset until you either lose or complete five in a row. If it's your 1st or 2nd match you'll actually play out the whole set and then try again for a deathless run?
I definitely quit after a death. It resets my score and I like giving someone the win if they kill off one of my units. It feels bad when you miss out on the 900 feathers.

NEVER GIVE UP, NEVER SURRENDER!

... unless you brought the wrong units to the battle, then surrender is ok.

I'll surrender if i brought the wrong team like most people here.
I get salty when its due to a dancer, just because I can never seem to get a hold of fighting vs dancers, they seem so bloody unpredictable, so I don't surrender in these cases, but I'll give the W to any other team.

Depends if I'm trying to get a high score or not. If you're trying to get a high score and don't restart after a death, then you're wasting dueling swords.

I finish the fight
And then immediately regret it because I have to spend an extra sword to reset my arena streak

Every... Fucking... Time

They have two different reasons. Those who quit after a single death are aiming for the highest arena scoring, and those who can't care less finish the fight regardless of how many casualties they have taken. I do not care for deathless runs, because I'm too lazy to redo all my 7 matches. With all that being said, is there really any point in knowing?

Usually I finish. Only time I surrender after a death is if my remaining units can't take out a certain opponent.

I finish the fight then do another round of 5 battles.

If I'm in deathless run mode, I'll give it to them after one kill. If I'm just trying to complete quests or dailies, I'll finish. Even wrong units, I'll finish.