Yes, low blood components are potential
side effects of all the CRAB drugs, including
Copaxone. It is called Thrombocytopenia. But, lowered levels of al the blood lines, red cells, white cells and platelets (called pancytopenia) was observed rarely before Copaxone was released.
As to how long the reaction of bone marrow suppression could last, I don't know.
Other things, like viruses can also lower the cell counts.
What are your doctors saying?