My suggestion is:
1. Observe what triggers her wanting sex (though minuscule she still has it)
2. How does she react to your advances (is she shy, mad, upset, wants to cry or laugh)
3. Does she even have any sexual fantasies (most likely she does even though they may not turn her on)
4. DON'T ever criticize for her lack of SD!
5. See a counselor and after that maybe even a doctor.
6. Make her feel loved and explain that you both will work on this "problem" and overcome it.
Here is my story:
I was married to a wonderful girl and we were madly in loved but she had a very low sex drive! After a long observation
I realized that she had an eating disorder (Bulimia).
I didn't put these two things together at a time (I wasn't mature enough at a time).
Though I wasn't at all selfish and tried to understand what was wrong in her or in me or both, it drew me mad how much I wanted to have normal sex with someone I loved.
Lesser I had sex with her more sexually abnormal I felt of myself.
Even though we both knew that she had a low SD, as her defense mechanism, she blamed me on being sexual athlete , wanting too much sex all the time.
I didn't wanna have sex when she "lets me have her" hence I thought it was wrong.
And I would retrieve to my masturbation which made her mad!
We were in catch 22 for both!
BUT when she wanted to have sex we had the best sex I ever had before!
After we divorced, by pure chance, I saw a talk show on Eating Disorders and realized that women affected by that have low or no sex drive.
Thus I concluded, that could have been the problem.
It was late to get back together (she had a bf by then).
One time after 4-5 years we met again, and I felt that i still was in love with her and we end up spending a night together.
OMG, we had it all night long, almost nonstop!
She confessed that her BF had a very low SD and he doesn't initiate sex, and when she does most of the time he rejects the intercourse by saying "Foreplay is more important to me then sex itself."
I asked her if she still had Bulimia and she said that she was cured few years back and since then she wanted to have sex almost every day.
Conclusion: I cant say that her disorder was to blame for her SD but I think there was something to do with her mental state at a time.
SO DONT CONFRONT HER BUT TRY TO TALK TO HER AND MOST IMPORTANTLY TRY TO UNDERSTAND HER. She knows that it is not normal but she doesnt wanna take a blame.
Good Luck