Thanks for such an clearly written question. Your partner's response to your request for more sex is what I call nonrelational. She's says,'There's nothing wrong with me, and drops the ball back in your lap.' She isn't willing to consider the fact that her lack of desire for sex has an impact on you.
If you have a problem with the lack of sex, then she has a problem as well--that is if she wants to stay with you. When a partner wants to keep the relationship, he/she must be willing to hear about the effect that his/her words or actions (in this case lack of action) has on the other.
To not listen, and to be unresponsive, is relationship destructive behavior. I will go a step farther and say that her behavior is quite hostile, and communicates a lot of anger. She is saying in action,'I don't care how you feel. Tough, you aren't getting any.'
Withholding sex is angry behavior. The only way to handle this is confrontation. You need to tell her that if she wants to have a relationship with you, then she needs to consider your needs. You can tell her that she may think that she has no problem, but since you have a problem, and she is your partner, your problem is necessarily hers as well.
Tell her that you are starting to think about sleeping with other people, and ask her if it is her intention to push you into another person's arms. Tell her that her unwillingness to have sex with you says that she is angry with you, and you want to know why.
Tell her that enacting her anger by withholding sex isn't going to solve the problem. It's just going to drive you away and break the relationship.
If you can get her talking about what has turned her off to you, then you have a chance of resolving the problem. You have a hard road ahead.
You need to overcome her denial that anything is wrong, and you need to teach her to talk about her anger instead of withholding sex as a way of communicating her anger.
If you can't get her to talk with you, then go to a couples therapist. I wish you the best.