I just don't see why it would prevent gravity from pulling everything together too much. If it acted in a way as to repel each neutron from the others, then it would prevent gravity from pulling them closer than 10^-15 meters apart, so that if matter was constantly being put into the system, the whole star would have a maximum density for a while until the strong force couldn't repel things enough to overcome gravity and the core would collapse. But this is not how it works as far as i understand.