Treatment for patients with autoimmune destruction of blood cells is poor. The part of the body that fights infections is called the immune system and white blood cells (WBCs) are part of the immune system. Normally, a person's body creates WBCs to fight infections and eliminates WBCs which have stopped helping the body function. Patients with autoimmune destruction of blood cells have difficulty eliminating old WBCs. The abnormal WBCs build up and can damage other healthy cells, which can lead to anemia, fatigue, jaundice, internal bleeding, infection, and cancer. Few effective medications exist for treatment for patients with autoimmune cytopenias and those commonly used are fraught with side effects. Nevertheless, as scientific understanding of autoimmune diseases has improved, more directed and less toxic therapies are becoming available. A number of groups have been studying the efficacy of a medication called sirolimus in patients with autoimmune diseases. This medicine has been FDA-approved for over 20 years. Sirolimus is a medicine used in children with other diseases. Sirolimus works, in part, by eliminating old and abnormal WBCs. Our group and others have shown that sirolimus is effective in mice with autoimmunity and in children with a rare condition called Autoimmune Lymphoproliferative Syndrome (ALPS). We believe sirolimus will help children with autoimmune cytopenias. We believe it will improve their symptoms and make them less sick. We propose to study sirolimus in children with chronic and/or refractory autoimmune cytopenias.