As early as possible. Whenever you get a premonition that your code is slowly turning into an ugly beast that is very likely to consume your soul and give you headaches, and you know the problem is in the underlying structure of the code (so any fix would be a hack, e.g. introduce a global variable), then it's time to start over.
For some reasons people don't like throwing away precious code, but if you feel your better off starting over, you are probably right. Trust your instinct and remember that it wasn't a waste of time, it taught you one more way of NOT approaching the problem. You could (should) always use a version control system so your baby is never really lost.
