What is the most common cause for white blood cells to get low?

Many causes: Depends, but most common is probably from viral infection. Many other possibilities including drugs, leukemia, other infections, benign cyclic changes......

Low white blood cell: The most common cause of a low white blood cell count is an infection, commonly seen with viruses. Certain viruses can suppress the ability of the bone marrow to make normal white blood cells. Once a person recovers from the infection, the white blood cell count will then recover (if this was the cause). There are many other causes of low white blood cell counts, some of them very serious.