Don't take no for an answer. Just because you're happy unmarried doesn't mean you couldn't be just as happy married. Let him know that getting married is important to you. If he thinks you don't care, he'll never get it together. Don't let it bother you that it's the third marriage for you both.
Many people find happiness in the fourth or fifth marriages.
You'll feel a stronger sense of belonging and commitment if you're married. So will he. And if something should come up where you need to be married to make decisions for emergiencies or health reasons, you'd want to be official. Also, you deserve the protection that a wife gets financially, socially, and emotionally. Just because a lot of things are great, doesn't mean you shouldn't get the marriage you want.