Well, perhaps as Steve says often, if we could perfect patience perhaps we'd be very close to enlightenment, but if we perfect concentration, it doesn't necessarily mean that we're going to be enlightened. This is because concentration by itself doesn't actually get us enlightened, according to my understanding. Otherwise the Buddha would have become enlightened under the ascetic teacher from whom he first learned. He perfected concentration to the highest level, but he still didn't become enlightened.
Why is patience a Parami? Perhaps because we need some wisdom in order to develop patience. Patience grows as one's understanding of cause and effect and Kamma grows. It grows as we develop the understanding that many things are beyond our powers to control, including this body and mind. We can control them a certain amount, but to do this we need a deeper insight into understanding the causes and conditions that bring about beneficial qualities and sow the causes for the arising of these things. Patience also grows as one's compassion grows, so it seems like we're talking about the first two factors of the Noble Eightfold Path - Right Understanding, which is Wisdom, and Right Thought or Intention, which is Compassion and Lovingkindness. When we have compassion and lovingkindness we're much more patient with others, because we understand how much Dukkha there is in the world. We have more patience with ourselves, because we realize that if we are not compassionate to ourselves then the results we want, don't arise. Compassion and wisdom greatly help with the growth of patience, so if we want more patience then it would be good to put more effort into the Compassion/ Lovingkindness meditation. It's also good to develop more understanding about Anatta, which we understand more as our understanding of cause and effect increases.
When considering how to strengthen patience, it's also helpful to look at the fourth Foundation of Mindfulness. The Buddha asks us to be aware of the Seven Factors of Enlightenment and the causes and conditions that bring these about, so that we can then cause them to arise again in the future and make them stronger. He also talks about the Five Hindrances, knowing how they arise and how to let them go. This is important, because we can bring up aversion towards the hindrances and hate the fact that we have desire and aversion and worry and fear, but that won't help us let them go. We have to understand the causes and conditions that help to let them go. With aversion we have to develop more Compassion/ Lovingkindness. With worry and fear we have to understand death and impermanence. There's a few more, but I don't have enough time to go into all of those now. Working on this level helps us to strengthen patience both with ourselves and with others. So with the growth of the Paramis, we also have to understand what helps to make them grow, and with Patience, what helps it to grow is developing more Compassion/Lovingkindness, and understanding how difficult it is for people to understand their own suffering and let it go, especially if they do not know any methods on how to do this.