So, this actually happened in our last session.
I offered the PC (through the fiction, via an NPC) the opportunity to Short Rest since they had been up the whole night through to the following morning. Had they taken it the opportunity, it would have led to their 3rd failure in the Skill Challenge, thus failing it completely.
Instead, they got an auto success (3/2) for remaining vigilant. Player was unaware of this auto success.
They opted to stay awake and see the next person who was brought in for questioning, which after a further 2 successes noticed something was off about the guard escorting the witness (5/2).
With some assistance they orchestrated an easy enough distraction (6/2) and were able to intercept an assassination attempt and through combat stop it.
I'm still surprised the player denied the Short Rest to refresh their abilities, but it worked out great in the fiction.