Accepted is the status of your tax return—not your tax refund.
Once your return has been accepted (received) by the government, they take over the refund status update duties, since they hold the purse strings. The status in TurboTax will remain as accepted.
Use the IRS Where's My Refund site for the latest word on your federal tax refund and your state government's refund lookup service for the latest on your state refund.