The closest approximation to the results for women was a question where we asked men how often they could go without any sexual activity. These results were interesting, and are shown below. Here we see that men who could go a year or so without any sexual activity tend to report low relationship quality. Then as desire increases in frequency we see a steady incline in relationship quality. However, there are two exceptions to this notion that higher desire is related to better relationships: men who could go forever without sexual activity of any kind report above-average relationship quality, and men who can't last a day without sexual activity report very low relationship satisfaction.
Why might that be? Maybe for the men who feel no sexual desire, sex is unrelated to their perception of relationship quality, and is determined by other factors. It might also be that for men with exceptionally high levels of desire, sex is a big issue in the relationship - any differences between partners' desire levels would be amplified here, and these men might feel very dissatisfied with their relationship as a result of this mismatch.
In the context of my research, I'd suggest that these findings are much more complex than "more sex = better relationships". It's very likely that better quality relationships would actually foster more sexual activity in the relationship. It's also likely that relationship quality is related to mood and stress, and desire and sexual function are also closely related to these factors, so this is just one piece of a very busy puzzle.
What do you think about these results? Do you have any questions like this one? I'm happy to dig through my data for answers...