To assess the safety and efficacy of subcutaneous sargramostim ( granulocyte-macrophage colony-stimulating factor; GM-CSF ) in increasing and maintaining the granulocyte count in HIV-infected children who have developed granulocytopenia as a result of continuous intravenous ( CIV ) zidovudine ( AZT ). To assess the short-term and long-term effects of concomitant GM-CSF on other hematologic parameters. To assess the potential therapeutic benefit of concomitant GM-CSF and AZT on the natural history of HIV infection and associated infectious complications.