"He exhausted himself trying to prove his innocence."
In the story, he was being accused, so when the 'jokers' would bring up the string he would become increasingly vexed by the fact that no one would believe him. You can also infer from the example of the soldier; a soldier telling the story of a battle might be painful, so if he is like a soldier telling of his battles, the claim of his innocence must also be an exhausting and painful story to keep repeating, since no one will believe. In the end, this is what led to his ill-being.
