The purpose of this research study is to evaluate a new investigational drug to prevent reoccurrence of neuroblastoma that is in remission. This study drug is called DFMO. The objectives of this study will be to monitor for safety and look at efficacy of DFMO. The safety of the proposed dosing regimen in this trial will be tested by an on-going risk/benefit assessment during the study. A patient benefiting from treatment, not progressing on therapy, and in the absence of any safety issues associated with DFMO may continue on treatment up to 27 cycles with the expectation that there will be an overall clinical benefit. The procedures involved in this study include Medical history, Physical exam, Vital signs (blood pressure, pulse, temperature), Blood tests, Urine tests, MRI or CT scan of the tumor(s), MIBG scans, and Bone marrow aspirations. All of these tests and procedures are considered standard of care for this population. Drug administration is also part of this protocol, including an investigational new drug called DFMO. The proposed dosing regimen is an oral dose of DFMO tablets two times a day for each day while on study. There will be 27 cycles. Each cycle will be 28 days in length.