The amendment offered by Rep. Davis last month also made little headway in the GOP-controlled House.
Rape is a growing concern for the Department of Defense and for the more than 400,000 women who serve in the U.S. military.
A Department of Defense report released last year showed that sexual assault in the military had risen by 11 percent in the past year, and by 16 percent in war zones. There were more than 3,200 such reported cases in that fiscal year.
"It's a sizeable concern," Rep. Davis told ABC News. "Sexual assault and abuse is a large concern for all the military services. Any of the services will tell you that. In fact, it's become quite a priority for them to address this issue."
"It's common for them [women] to have been assaulted and raped than it is to have been injured in battlefield," she added.
The stigma that's associated with sexual assault, and the added dilemma of confidentiality and of being ostracized by peers and commanders, also prevents many women from speaking out about their traumatic experiences.
"It was an environment where you are scared to ask about anything," Kenyon recalls of her own experience. "Saying something like that would have probably got you a court-martial."
Kenyon's pregnancy eventually ended in a miscarriage on the plane back to the United States, as did her military career.
"It's a disgrace, especially when it comes to rape and sexual assault, that this option is not available," said Kenyon, who left the military in 2006 and now works with victims of military sexual abuse. "To leave them unprotected and out of options, I think it's a big betrayal to the women who were assaulted."
When asked about the proposed bills and the push by abortion rights groups, a spokeswoman for the U.S. military said "the department will continue to follow Congressional mandate regarding the funding of abortions and restrictions regarding abortions conducted in DOD medical treatment facilities."