Is repeated failure in exams a matter of divine decree and destiny, or due to personal shortcoming, especially in the case of forgetting to cross out the question number?

Everything that occurs in the universe is by Allah's divine decree and destiny. The servant is commanded to take permissible means and exert their utmost effort. If what they hope for is not achieved, they are not to be blamed. Destiny is a hidden secret, so one cannot definitively assert that they will not succeed if they fail. It is legislated to repeat the attempt along with performing the Istikhara prayer.