This phase I/II trial studies the side effects and best dose of 8-chloro-adenosine and how well it works in treating patients with acute myeloid leukemia that has returned after a period of improvement (relapsed) or has not responded to previous treatment (refractory). Drugs used in chemotherapy, such as 8-chloro-adenosine, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading.