Inclusion Criteria:

• No greater than 25 years of age when originally diagnosed.
• Histologic verification of condition.

• Has recurrent/progressive; or resistant/refractory neuroblastoma with at least ONE of the following:

  1. Measurable tumor on MRI or CT scan or X-ray (at least 20 mm in at least one dimension) or
  2. MIBG scan with positive uptake at minimum of one site, or
  3. Bone marrow with tumor cells seen on routine morphology (not by NSE staining only) of bilateral aspirate and/or biopsy on one bone marrow sample.
• Has Lansky or Karnofsky score of 60%, and a life expectancy of > 2 months.
• Has fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy.
• Has not received treatment with myelosuppressive agents within 3 weeks and with any biological therapy within 2 weeks of study entry.
• Has not received radiation for a minimum of four weeks prior to study entry at the site of any lesion that was biopsied to document study eligibility.
• Patient is 2 months post myeloablative therapy and autologous stem cell transplant.
• At least six weeks must have elapsed since treatment with therapeutic doses of MIBG.
• Patients who have previously received combination bortezomib and irinotecan are ineligible but can have received one of the drugs.
• Must not have received hematopoietic growth factors within 2 days of study entry.
• Cannot be receiving enzyme-inducing anticonvulsants (phenobarbital, phenytoin, carbamazepine).
• Concomitant radiotherapy to painful bone lesions will be allowed (excluding intestinal tract, spine or pelvis) but other non-radiated sites of measurable disease must be available to assess response to chemotherapy.
• Patient has adequate bone marrow function (defined).
• Patient has adequate renal function (defined).
• Patient has adequate liver function (defined).
• Post-menarchal females must have a negative beta-HCG. All males and females must use effective contraception during study.

Exclusion Criteria:

• Patient is status post-allogenic stem cell transplant.
• Patient has uncontrolled infection or active diarrhea defined as 2 or more stools per day greater than baseline.
• Presence of HIV, active hepatitis B, or active hepatitis C infection.
• Pregnancy, as determined by B-HCG measurement.
• Grade 2 peripheral neuropathy within 14 days before enrollment.
• Myocardial infarction within 6 months prior to enrollment or various other indications of heart disease. (defined)
• Hypersensitivity to bortezomib, irinotecan, cefixime, boron or mannitol.
• Female subject is breast-feeding.
• Serious medical or psychiatric illness likely to interfere with participation.
• Patient has received other investigational drugs within 14 days before enrollment.