Games : At what point would a site be better to restart than to continue on?

http://chat.stackexchange.com/transcript/message/20849460#20849460

Murgatroid99 made a comment on how in all cases it is never worth restarting, and that trudging forward is the best option in any scenario.

Is that really true? Is there a point where it would be far more valuable to start over at square 1 as opposed to continuing on with low scores in everything else?