The purpose of this research study is to study the effects of using aromatase inhibitor (AI) therapy intermittently on participants with breast cancer. AIs are a class of drugs used to treat breast cancer in postmenopausal women. They work by decreasing the level of estrogen, which is believed to stimulate the growth of tumor tissue. Breast cancer that progresses despite therapy with an AI is thought to have become resistant to AI therapy. There is scientific evidence to suggest that resistant breast cancer cells learn to grow at the very low levels of estrogen present on AI therapy, and that increasing estrogen levels even slightly by stopping AI therapy may inhibit the breast cancer cells.