My mother has a low blood count, and is always getting infections, what are the possible causes?

Several things : Low blood counts can mean low red blood cells, white blood cells, or platelets. I assume she has low white cells if she's getting infections. Causes include medications, past chemotherapy, or a bone marrow problem called myelodysplasia. Some chronic leukemias can cause low white blood counts. Her doctor should look at her blood smear under a microscope to see what's going on.