When I respawned, he was still marked hostile, but absolutely refused to continue to match when I re-entered the arena, mumbling something about his glass cockpit BSODing. Not really, but you get the idea.
I spared his life, docked with the arena building; the manager was distraught (failed arena battle), but still allowed me to challenge Stormbringer again.
Which respawned Stormbringer at full health, yes, but he didn't try blowing me to pieces from the get go. Seems he's too busy reinstalling his cockpit's OS to do anything:

(screenshot taken after realizing that he isn't firing back, and 30 seconds of, um, waiting. All he did was jet away from me for a bit, but nothing else.)
I put Stormbringer out of his misery. >_>
Unfortunately, the next opponent ran on Linux and I died. <_<