It sounds like a sloppy thing to measure; but Martin Seligman (learned helplessness/learned optimism) has quizzes to measure optimism/pessimism, which have experimentally demonstrated predictive power (and actually have been used to supplement job interviewing, with measurable success). So measuring determination might be possible. There's even checks to prevent/detect cheating. Of course, extra smart candidates with million dollar (VC) motivation may quickly subvert any a test. Still, it would be interesting, intellectually, to see if it did work.
Might also be interesting to ask one of Seligman's students to assess YC candidates for optimism (his definition means that you bounce back from failure with energy - e.g. a pivot). It seems plausible to me that that would also be predictive of startup success (and also predictive of determination - the ability to keep going).