This phase I/II trial is studying the side effects and best dose of VEGF Trap when given together with docetaxel and to see how well they work in treating patients with persistent or recurrent ovarian epithelial cancer, primary peritoneal cancer, or fallopian tube cancer. VEGF Trap may stop the growth of tumor cells by blocking blood flow to the tumor. Drugs used in chemotherapy, such as docetaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving VEGF Trap together with docetaxel may kill more tumor cells