An infertility clinic has offered Corporal Wilson and Ms. Black a discount, and friends have started a GoFundMe website to help pay for the treatment. But Ms. Black said: “It’s very taxing when you have to come up with such a large amount to even try to have a family. The fertility issues arise 100 percent from his combat-related injury.”

Senator Patty Murray, Democrat of Washington, has been trying for several years to change the law. “This is a widely used medical procedure, and our veterans should have access to it,” she said. “This is an issue between the veteran and the spouse and their doctor.”

The V.A. supported legislation by Ms. Murray to change the law, provided that money was allocated pay for the services, according to testimony last June before the Senate Committee on Veterans’ Affairs by Dr. Rajiv Jain, a V.A. assistant deputy under secretary.

It looked as if the bill was heading to a vote, but Ms. Murray withdrew it in July because a group of Republicans, led by Senator Thom Tillis, Republican of North Carolina, had added amendments that would have, among other things, prohibited the V.A. from working with Planned Parenthood and other groups that provide fertility services and perform abortions. The amendments were a reaction to videos released by anti-abortion activists who accused Planned Parenthood of selling fetal body parts.

Ms. Murray has vowed to keep trying. “I’m never going to give up until we get this done,” she said. “I believe it is so essential for these young men and women to know their country is behind them when they get home, and their dream is not taken away.”

But for many couples, the biological clock is ticking. Ms. Murray acknowledged that for some, who had asked for her help years ago, it is already too late.

Army Staff Sgt. Michelle Wager was injured by a roadside bomb in Baghdad in 2007. She lost one leg and had severe damage to the other. She has sustained fractured vertebrae and a brain injury.

“Once I was at Walter Reed and sort of conscious, sort of understanding what was going on, I realized that I stopped having periods immediately,” Sergeant Wager said.

She was only 31, and her menstrual cycles had always been normal, she said. But the injuries seemed to plunge her into menopause, complete with hot flashes. Initially, military doctors reassured her that she would remain fertile. But the changes troubled her, and she sought treatment. Drugs prescribed in 2011 brought some irregular periods. A doctor told her that if she wanted children, she should try to get pregnant as soon as possible. But she had no partner.

“My options were to pick a donor out of a book,” she said. “I wasn’t quite prepared for that.”

Later, she started a new relationship, and in October 2014 became pregnant. But she miscarried.

“We’ve had baby fever ever since,” she said.

But she and her husband have not conceived again. In a letter written to help explain her condition to the V.A., her gynecologist said, “In my professional opinion, her infertility could likely be explained by her traumatic injuries that she suffered while serving in Iraq.” He went on to say that the brain injury had probably caused her to stop menstruating, and that he had referred her to an infertility clinic.

Even though the V.A. does not provide in vitro fertilization, Sergeant Wager said she hoped it would recognize her infertility as a service-related injury and provide compensation, which she could use to pay for the treatment she needs.

“I’m dumbfounded,” she said. “We’re just sort of at the end of our rope here, not sure where to go or where to turn.”

She and her husband have been seeing an infertility specialist, paying out of pocket. The clinic donated one attempt at intrauterine insemination a few months ago, but it failed, and the doctor told the couple that their best bet, probably their only one, was I.V.F. They cannot afford it, and are considering borrowing the money from a finance company that lends to couples having I.V.F. She is now 40, and time is running out.

“We’re not the richest people, and for something that’s not guaranteed, it’s a little bit scary,” Sergeant Wager said. “But we’re not ready to give up yet, either.”

In November, the American Society for Reproductive Medicine, a professional group for fertility doctors, called the ban on V.A. coverage “antiquated and unconscionable,” and said that many of the country’s leading infertility clinics would offer “deeply discounted” care to veterans with service-related injuries that had diminished their fertility.

Kathleen Causey, whose husband, Sgt. First Class Aaron Causey, had an injury to the testicles that impaired his fertility, called the discounts “wonderful and gracious.” But she said: “We shouldn’t have to rely on people’s kindness to have children. Where is the support of the V.A.? Why isn’t Congress taking this seriously?”

She added, “We’re only in this situation because he chose to serve his country, and now his country is not taking care of him.”