I think you can deduct this expense. It is common practice for businesses to have corporate cards. If there is a charge for such a card, so be it, you should be able to deduct it since it is a business expense.
The IRS should not tell you that you can get the Discover Card instead and not pay charges.
My rationale is this: you can take a business expense deduction on your office space. If you are in Manhattan, this will cost you much more than office space in Arkansas. As a result, your deduction for doing business in Manhattan will be higher. The IRS will not challenge your deduction and tell you to move to Arkansas....
I believe that if you demonstrate that most of the charges on the account are for business, then you're good.