This purpose of this study is to evaluate the safety and effectiveness of a technique called focal high-dose-rate (HDR) brachytherapy as treatment for prostate cancer that has come back in the prostate after prior radiotherapy. The study will examine the safety and efficacy of the treatment. The type of radiation that participants in this research will receive is targeted directly at the areas of the prostate where recurrent disease is evident, while avoiding treatment of the normal appearing prostate. This involves the placement of a radioactive material in the affected area of the prostate temporarily, where it remains for a short period of time, and then is subsequently removed using a minimally invasive technique called HDR Brachytherapy.