He's constantly going to his death and because he doesn't learn from it and change things, he keeps realizing just before, sends the note to his younger self to start on the path again...

This almost has me thinking of Matrix Reloaded when Neo got to the Architect. There'd have to be a point in time where Doctor learned from his actions and consequently lead to a better ending for himself and as many other people as possible. If that makes any sense. And it would go along with the whole thing of 'Time can be rewritten.'