Sometimes blood levels of prostatic specific antigen (PSA) will rise in men who have had prostate surgery or received radiation therapy for localized prostate cancer. A low value for the PSA is more desirable as is may indicate no tumor growth. Giving the hormone therapy intermittently (in cycles of treatment and off treatment periods) appears to delay the change of prostate cancer to a type of prostate cancer that resists hormone therapy. If it does, the prostate cancer will be treatable for a longer period of time, as well as improve the quality of life. Mental functioning is monitored during therapy to see if this treatment has any impact on memory or ability to carry out tasks. In addition, extra tubes of blood are obtained to test for Amyloid-B protein (AB protein) whose presence may be associated with problem solving decline.