Inclusion Criteria:

* Age 0 to 21 years
* Child should be receiving ongoing care with pediatric hematology/oncology providers
* Confirmed diagnosis of any of the following

1. aplastic anemia

* Diagnosis of severe Aplastic anemia is established if Bone marrow cellularity \<25% or and at least two of the following criteria are met:- (i) absolute neutrophil count less than 0.5 × 109/L, (ii) platelet count less than 20 × 109/L, and (iii) reticulocyte count less than 20 × 109/L
* Moderate aplastic anemia is defined as bone marrow cellularity \<50 percent and depression of at least two out of three blood counts below the normal values: criteria are met:- (i) absolute neutrophil count less than 1200/mm3, (ii) platelet count less than 70,000/mm3, and (iii) anemia with hemoglobin less than or equal to 8.5 g/dL and absolute reticulocyte count less than or equal to 60,000/mm3 in transfusion-dependent patients but not fulfilling the criteria of sever aplastic anemia
2. refractory cytopenia of childhood without monosomy 7 or 5q- and without an evidence of cytogenetic abnormality with predisposition to leukemia
3. myelo-suppression specifically thrombocytopenia as defined by primary oncologist in children with solid tumors secondary to chemotherapy or radiation therapy contributing to delay in chemotherapy
4. myelo-suppression contributing to severe pancytopenia (absolute neutrophil count \<0.5 x 0.5 × 109/L; platelet count less than 20 × 109/L, and reticulocyte count less than 20 × 109/L secondary to any other drug or infection
5. patient undergoing stem cell transplantation and experiencing persistent thrombocytopenia (platelet count \<10 x 109/L) requiring platelet transfusions
6. diagnosis of inherited bone marrow failure without chromosomal fragility disorder
* Adequate organ function within 7 days of enrollment defined as:

1. Creatinine: ≤ 2.0 mg/dL
2. Hepatic function:

* For arm A, elevation of liver enzymes is acceptable for patients with hepatitis induced SAA as long as patient does not have history of chronic liver problem. If necessary, liver biopsy will be performed.
* For Arm B, elevation of liver enzymes will be accepted as long as no chronic liver problem. Liver biopsy will be performed if necessary.
* Females of childbearing potential agree to use effective contraception during the study period and for 4 months after completion of therapy
* Must be able to provide written and voluntary informed consent.

Exclusion Criteria:

* Gestational age \< 32 weeks or Age ≥ 21 years at the time of study enrolment
* Preexisting condition with predisposition for thrombosis
* Diagnosis of bone marrow failure syndrome with cancer predisposition including chromosomal fragility disorders (Fanconi anemia, Bloom syndrome, Ataxia Telangiectasia) and other conditions with known association towards cancer predisposition
* Presence of complex karyotype or monosomy 7 or 5q- or other cytogenetic abnormality with known predisposition to cancer.
* Diagnosis of MDS
* Female subjects who are nursing or pregnant (positive serum or urine β-human chorionic gonadotropin \[β-hCG\] pregnancy test) at screening or pre-dose on Day 1.
* Current alcohol or drug abuse.
* Treatment with an investigational drug within 30 days or 5 half-lives (whichever is longer) preceding the first dose of study medication.
* Active and uncontrolled infections (e.g. sepsis, hepatitis B, hepatitis C).
* Chronic liver disease ie. Fibrosis or cirrhosis
* Subjects infected with Human Immunodeficiency Virus (HIV).
* Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to Romiplostim that contraindicates the subjects' participation
* Known history of sensitivity or allergy to the active substance, to any of the excipients, or to any E. coli-derived product.
* Moribund status or concurrent hepatic, renal, cardiac, neurologic, pulmonary, infectious, or metabolic disease of such severity that it would preclude the patient's ability to tolerate protocol therapy, or that death within 7-10 days is likely.
* Subjects who have participated in any study using an investigational drug during the previous 30 days.
* Non-English-speaking families who cannot speak or read English