On Tuesday, Macy's CMO Martine Reardon said the reason the store will not drop licensor Donald Trump, despite his bizarre allegations that President Obama might not be American, is because Macy's listens more closely to its shoppers than to the media. (Or to online petitions calling for Macy's to drop Trump.)

She might want to listen again. New data from YouGov BrandIndex shows Macy's approval rating among women over 18 has plunged dramatically in recent weeks. Now, it's even below that of troubled discount giant JCPenney.

Speaking at our Ignition 2012 conference in New York, Reardon said:

"We try to separate from that and we try to let the customer vote on that ... As long as that customer is still voting by wanting to buy that product, then that's what it's all about."

Here's YouGov's tracking of Macy's reputation in its core demographic: