Cuz Republicans don't have anything else to use against her. This whole thing started back when she first ran for Senate against Republican Scott Brown who had won a surprising special election to fill the seat of the late Ted Kennedy. He had nothing to run against Warren on and found this old listing of her as Native American. Republicans since have taken that up.
It's not all strategic, however. I think it also fits into Republican Notions that Democrats, particularly left-wing ones, are inherently dishonest. It also fits in with there discomfort with people of color and with affirmative action programs. They think, falsely, that Warren obtain some sort of professional Advantage by claiming to be Native American. This fits in with their criticism of liberal programs which they feel give minorities, or in this case someone claiming to be a minority, and unfair advantage