This phase II trial is studying how well giving trastuzumab together with ixabepilone works in treating women with HER2-positive metastatic breast cancer. Monoclonal antibodies, such as trastuzumab, can locate tumor cells and either kill them or deliver tumor-killing substances to them without harming normal cells. Drugs used in chemotherapy, such as ixabepilone, work in different ways to stop tumor cells from dividing so they stop growing or die. Combining trastuzumab with ixabepilone may kill more tumor cells.