Dr. Gouge (whose manual, Domesticall Duties I've been reading) also took the systematic approach to the duties of married people. He begins with, "Who may seek to be married?" and after proving to the last breath that humans must marry only other humans (no going to the altar with Rover), he goes on to more relevant matters.
One of the first of Gouge's qualifications for marriage is they must be able, physically, to have sex.
More specifically: "They are to be accounted impotent and in that respect perform the essential duties of marriage, who . . . were born eunuchs from their mother's womb (Matt. 19:12); or by any accidental occasion are so made: as they are defective, or closed in their secret parts, or taken with an incurable palsy [paralysis]; or possessed with frigidity [lack of all sexual desire] . . . These ought not seek after marriage: for by those signs of impotency God sheweth that he calleth them to live single." (The bracketed comments above are mine.)
It appears that Gouge's definition of "impotence" could apply to men or women, depending on the situation, though I would guess it got a different name when dealing with a female problem. Gouge seems to be most concerned over a man or woman going into marriage knowing that sex was impossible because of a physical problem. When Puritans formed their experimental communities in New England, they made impotence a potential grounds for divorce.
So why was sex so important? First of all, impotence would frustrate one of the goals of marriage: having children.
So does that mean that if a woman could not conceive, she had failed in God's purpose and her husband might divorce her? Absolutely not. Infertility, or "barrenness" as it was known in that era, was completely different from impotence. For one thing, infertility could be discovered only after the marriage had been in place for at the very least some period of months, as opposed to the impotent person who presumably would know that s/he could not consummate the marriage even before the wedding night. So an impotent person was deceiving his or her spouse from the beginning.
Further, having children was not the only goal of marriage: "so inviolable is the marriage bond, that though it be made for children's sake, yet for want of children it may not be broken." And sometimes a woman who was barren for many years even would become -- un-barren. The Bible was full of stories of women who could not have children for many years, and then "her womb was opened."
But there was another matter, too: a barren woman could still love her husband physically -- could "yield due benevolence" [Gouge's euphemism for sex] -- and an "impotent" one could not. Gouge makes it clear throughout Domesticall Duties that part of the purpose of sex is to bring the husband and wife together for love and pleasure. Married couples should "mutually delight each in other, and maintain a pure and fervent love betwixt themselves, yielding that due benevolence one to another which is . . . ordained of God for this particular end."
It is also another gentle reminder to us that Puritans were not anti-sex. These people were not Victorians. They were Elizabethans (or nearly); very close to the age of Shakespeare. A Puritan teacher like Gouge might need to use euphemisms to talk about sex, but the topic was very much on the table for discussion, not hidden away or dismissed as dirty. In the seventeenth century even people who got a label like "puritan" were very clear on what helped make a happy marriage tick.