A theory which I believe explains this is the ground-breaking work that Carol Dweck has done on mindsets and how they relate to performance.
To recap, People can have either a fixed mindset where they view abilities as fixed, are more driven by performance goals and use helpless strategies when confronted with tasks beyond their capabilities. If given a choice between task beyond their capability and one beneath their capability they will choose latter. If forced to do a task beyond their capability, they will not persist too long and give up early- and not put too much effort as putting efforts shows that they don't have the talent.
The other mindset is a growth mindset which sees abilities as malleable, are more driven by learning goals, and use mastery or hit-and trial and persistent strategies when confronted with a task beyond one's capability.
It has been shown that one can be put into a growth or a fixed mindset by very easy manipulations like praising for effort rather than talent.
Given that fixed mindset is also performance driven, there is a high probability that rising the stakes high focuses one on performance goals at the cost of learning goals and primes one with a fixed mindset. Ask any person preparing for a high stakes exam whether he wants to learn the subject matter or get good score and you'll see what mindset a high stakes competition entails.
Given that performance motivation or fixed mindset is detrimental for hard task (task just beyond ones abilities); its no wonder that performance deteriorates as rewards loom large for non-rudimentary tasks.