The Mad Doctor is the name of the man who processes Thick Blood into stat-augmenting serum. He chiefly does this by operating a machine that seemingly strains the plasma out of the blood; however, it is a somewhat sensitive contraption, as it can only handle so large a volume of the fluid before breaking down. This causes the Mad Doctor to attempt to correct the problem, hit it futilely, and then give up, hanging an "Out of Order" sign across it and walking away.
Thick Blood does not carry over to the next stage, so it is in the player's best interest to reach this breaking point every single time. The machine's limit does increase each stage, allowing the player to become successively more powerful over the course of the game, but there is still not enough serum in the game to power up every character fully. This leaves leveling, to some degree, up to the player's personal discretion.