This study will combine an oral drug called DFMO with celecoxib (also oral) and two IV chemotherapy medicines called cyclophosphamide and topotecan.

• To find the highest dose of DFMO that can be given with celecoxib, cyclophosphamide and topotecan without causing severe side effects.
• To find out the side effects seen by giving DFMO at different dose levels with celecoxib, cyclophosphamide and topotecan.
• To measure the levels of DFMO in the blood at different dose levels.
• To determine if your tumor gets smaller after treatment with DFMO, celecoxib, cyclophosphamide and topotecan.
• To determine if specific gene changes in you or your tumor makes you more prone to side effects or affects your tumor's response to the combination of DFMO, celecoxib, cyclophosphamide and topotecan.
• To determine if the amount of normal chemicals in your body called polyamines go down in response to DFMO, celecoxib, cyclophosphamide and topotecan, and whether you are more likely to have a good response to the treatment if they do.

Inclusion Criteria:

• Patients must be > 2 years and < 30 years of age when registered on study.
• Patients must have recurrent/progressive high-risk neuroblastoma, refractory high-risk neuroblastoma that had less than a partial response to standard treatment or persistent high-risk neuroblastoma that had at least a partial response to standard treatment.
• All patients must have at least ONE site of evaluable disease.
• Patients must have adequate heart, kidney, liver and bone marrow function.
• Patients who have bone marrow disease must still have adequate bone marrow function to enter the study.
• Patients with other ongoing serious medical issues must be approved by the study chair prior to registration.

Exclusion Criteria:

• Females of childbearing potential that do not have a negative pregnancy test.
• Patients that are pregnant, breast feeding, or unwilling to use effective contraception during the study
• Patients status post allogeneic stem cell transplant.
• Patients who, in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study.
• Patients with disease of any major organ system that would compromise their ability to withstand therapy.
• Patients who are on hemodialysis.
• Patients with an active or uncontrolled infection. Patients on prolonged antifungal therapy are still eligible if they are culture and biopsy negative in suspected radiographic lesions and meet other organ function criteria.
• Patients with active bleeding of the GI tract or patients who have symptoms associated with stomach irritation (known as gastritis).
• Patients who have had a seizure within 12 months prior to enrollment and patients receiving anti-convulsant therapy for a seizure disorder.
• Patients with known Aspirin-Hypersensitivity triad (asthma, allergic rhinitis, ASA hypersensitivity).
• Patients with known hypersensitivity to celecoxib or other NSAIDs, aspirin or sulfonamides.