The context shows persistence and firmness of purpose despite repeated failures.
- “Resolute” means firmly determined. \(⇒\) Fits perfectly.
- “Obstinate” means stubborn, often in a negative sense.
- “Relentless” means not giving up, but is usually harsher and doesn’t fit as smoothly.
- “Unwavering” is close, but “resolute” is the best single-word fit here.
Thus, the correct answer is resolute.