This randomized phase III trial studies how well aspirin works in preventing the cancer from coming back (recurrence) in patients with human epidermal growth factor receptor 2 (HER2) breast cancer after chemotherapy, surgery, and/or radiation therapy. Aspirin is a drug that reduces pain, fever, inflammation, and blood clotting. It is also being studied in cancer prevention. Giving aspirin may reduce the rate of cancer recurrence in patients with breast cancer.