Recently having read Sir Thomas Wyatt's sonnet, "The Long Love," and Henry Howard's "Love that doth reign and live," I would suggest that though both men choose to love, they also prefer to avoid "commitment."
I understand that both men wrote their poems in response to Petrarch's sonnet 109, but I would assume that they chose to do so because something in the original sonnet spoke to them. Each man talks of the love in his heart for a woman, but each heart of each man chooses to flee from the presence of love, and to live a life that does not require the difficulties of being in a solid relationship. I would assume from reading these poems, that both men have commitment issues.
However, Wyatt's biography indicates that he had a wife and a mistress as well. Henry Howard, Earl of Surrey, was also married, so that it seems neither man repudiated marriage. However, marriage and emotional commitment are not always the same thing. Each man's wife bore him a son, an important aspect of a man's legacy and a woman's duty at that time: to make certain the family name lived on.
I would assume from these poems that an emotional commitment might have put each man off, but that marriage was not necessarily an emotional commitment. That is not to say that at some point before each man died, that he might not have changed his mind. And in light of the fact that each man wrote in response to another poem, perhaps the exercise was "academic" and not relevant to their personal lives at all. However, the poem they both chose to respond to could arguably have had a more personal meaning for each.