Were it an unconstrained equation, the maximum happiness would likely be greater. That is, there is a greater change of you finding an even better match--and hence deriving a greater level of satisfaction--if you were completely unrestrained. If you didn't have a job, responsibilities and such, and you could spend your entire life in pursuit of true love. And you would have a greater change of finding it.
At a more micro level, suppose your entire realm of existence constituted a particular bar filled with people. Further, let's say you spotted someone very attractive heading into the VIP area. You tried to go after that person, but the bouncer would not let you in under any circumstances. That is a constraint that's preventing you from meeting someone who very may well be the love or your life. Really, the greater area and time you can cover, the more of a chance you have of meeting this person.
Then, however, T-Rex considers another issue. He claims that if you've been with someone for long enough such that you've developed a considerable amount of history (and that this person makes you very happy), then even if you were to meet someone who you were more compatible with, it would not rationally make sense to trade up. According to Rex:
Let's say you're happy with Person A (95% perfect) and you meet Person B who is 99% perfect. It doesn't make sense for you to leave Person A for B if you've been with them for years! You lose out on all your shared history, and that's like a times two multiplier! [...] Romance with a times two multiplier!
The thing is that this argument depends on a little more than how long you have already been in a relationship. In fact, it makes some implicit assumptions. The first thing it assumes is that love/satisfaction is an constantly increasing function of time. Moreover, it seems to be an exponentially increasing function in this case. What T-Rex seems to be saying here is that as time goes by, you build a history and develop shared experiences with your significant other. These experiences give you pleasure as they occur, but moreover they continue to give you pleasure after they occur so long as you can share and relive them with that person. In a way, you're compounding these events. If you suddenly left this person, then you would no longer have someone to share these experiences with and hence they would lose some meaning. Consider an inside joke with your girlfriend or boyfriend. This joke would obviously not bring you the same satisfaction if you retold it to someone else. I believe this is why T-Rex refers to the cost of leaving Person A as "losing out on all your shared history."
Of course, depending on your view of romance, this might work differently. For instance, the "love/time" relationship might be more in shape of a logistic curve.
First, the curve increases slowly (likely to reflect the start-up costs of any relationship: anxiety, learning new things about them, etc.), then increases by a larger amount (to reflect the comfort stage of a relationship) and then it levels off (when you start getting bored). With this curve, it is entirely possible that an individual reach a level in his relationship where new and shared experiences bring little to no additional pleasure. It is even possible for curves to start to decrease! It is at this point that people consider leaving to find new, potentially greater experiences.
For simplicity, let us assume that the love curve is increasing and exponential (i.e. increasing returns to scale). Then, you would intuitively assume that you would only want to leave Person A for Person B if your love function with B increased at a higher rate than with A. However, this is really only true if you have enough time left in your life span in order to realize these benefits.
This brings us to another crucial element of what T-Rex is saying. Since there is a cost associated with breaking up with Person A, then in the short-run you would lose out. However, since satisfaction is increasing with time, then it would make sense in the long-run to leave Person A given that you do have the time to compensate for the loss you experience. Consider the following graph that reflect this:
In this graph, Person A is the red line, Person B is the blue line, and Person C is the green line. Suppose that you meet Person B relatively early in your life span. As you can see, it is possible that in the long run, Person B's function would cross Person A's function (at age x) and attain a greater happiness in the long-run. However, suppose you meet person C. Despite the fact that person C's function is increasing more rapidly than Person A's and B's, the fact that you meet person C so late in the game does not leave you enough time to hit the same level as A or B (before your unfortunate death at the hands of the end of the graph).
Therefore, if we make the assumptions that we did in this argument, then T-Rex is certainly right about having an incentive to stay given that you do not have the time to reach that level of satisfaction with anyone else. However, if there is enough time, then just the opposite could be true.
Ah, the good ol' romance multiplier. Incidentally, I'm a relatively young guy. I keep trying to make this argument to people I break up with, and they only end up getting mad at me. What's the deal?
Update: This also varies based on whether you're trying to simply attain a higher level of happiness in the long-run or whether you're trying to achieve an overall greater total happiness throughout your life. If the latter, then before breaking up, you would want to make sure that you have enough time in your life to both attain a higher level of happiness than you would with Person A and sustain that level of happiness for a while until death.