I just wanted to chime in here to say, in my experience, it seems many of the people I have met here don't feel the need to get married. Unmarried partners are given the same respect here as a spouse, and many people live together for a very long time without feeling the need to take that step. In America, at least in the Bible Belt portion where I am from, living together without being married is often seen as inappropriate or a "sin" and more people are pressured to take that step, by society or their families, or what have you. Here, people also live with their parents longer. In the states, it seems that people can't wait to get out of their parents' house and live on their own or with their mates (and their parents encourage them to move on, usually when they finish high school - they go away to college or move out), but here it is perfectly acceptable to live with your folks all the way through your twenties, or even longer, if you want. I think there is a lot less pressure involved with the way people live their lives in general. There is a tendency not to rush things like moving out or moving in with someone else or getting married, for that matter.
Also, factor in the "I don't want to get married just for the sake of the visa" thing, and that makes it rather hard to take that step. I think the pressure that a British partner might feel (who has otherwise not faced this sort of pressure) can be a bit overwhelming. Where normally he or she is allowed to take all the time in the world (many people I know here were living with their partner for 5 or 6 years before getting married, if they got married at all) they are suddenly faced with a dilemma of moving faster than they normally would in order to be together completely, or to just deal with the trials of LDR until they are ready to make that commitment.
In Becca's case, it's nice that she has had the opportunity to live with her man for a while, at least, to see how they get along together before making bigger commitments. My DH and I had never been in the same place together for longer than 2 weeks, even after we were married, until I moved over here a few months after our wedding. Not knowing what living together would be like was a big question in my mind. Fortunately, it all worked out perfectly, and we knew we wanted to be together.
I still can't believe it myself that he wanted to get married - that he proposed so soon and was so sure of what he wanted, and he said the visa had nothing to do with it. He had been married once before (to someone he was with for 6 years before the wedding) and the marriage itself only lasted a year, then he had another partner for 5 years, they had a child together, and he hadn't asked her to marry him. Pretty shocking, but I have to say, he must be the exception rather than the rule. Knowing what I know now about the culture of relationships and commitments here, I am very surprised he was so ready to take that step so soon. I feel lucky that we weren't stuck in limbo like many others, but I would've waited forever for him to be ready, if that had been the case.
I think it's best to just be patient, and know that it isn't "you" or anything like that, and most likely, your partner might be a bit afraid to move so quickly, as that is something that doesn't happen as often here - the whirlwind romance of meeting and getting married a few months later isn't the norm here. Even DH's parents cautioned him against moving too fast, and thought I should try living here with him rather than being married (which is funny to me, as my parents always gave me so much grief when I lived with a boyfriend without being married). I am sure one day they will tire of LDR and decide it's better to go ahead and take the plunge in order to make things easier to be together. But you are right, it sucks to have to get married in order to live in the same place, but often that is the only option. Good luck to everyone who is still waiting for their moment!