This photo from the archives (click on it for a larger version), from when I was a brown belt in 1992 or so, shows me about to break a cinder block cap during a intramural tournament. It's not a terribly impressive break -- I really need to be in a lower stance and drop my center of gravity more -- but you may notice that I'm performing the break with my left hand. And I am not left handed.
The reason why I am doing this left handed is not because I am some sort of Inigo Montoya of tameshiwari and needed an extra challenge to keep myself from getting bored, but because I had injured my right hand trying this break a few weeks before. That time, I managed to break the cap but badly bruised the pisiform bone in my right wrist when I hit the target wrong.
As I was still healing from that, I decided to use my left hand when the tournament came around. And once again, I hit it wrong, broke the cap but bruised the same bone in my other wrist.
Sometimes in martial arts training, the line between persistence and stupidity can get blurry. We have to train to not give up, but we also have to train to not repeat our mistakes. Developing the discernment to know the difference is one of the greatest challenges we face, both as students and instructors -- should we push ourselves or our students to keep going through the mental challenges of exhaustion and pain, or should we stop before a bad habit gets set or there is a real injury?