Accepted in TurboTax just means that they have received your return but have not processed it yet. This is normal; until they start processing it on their own, you won't find record of it when tracking on their website. So if you try to look up your refund status, don't be surprised if they tell you "no record found."
The accepted status in TurboTax will remain the same from here on out, since we no longer deal with the return once the state or IRS receives them.
IRS representatives will be able to research the status of your refund since your return was accepted more than 21 calendar days ago. Call them at 1-800-829-1040, but prepare for potentially long wait times.
The following TurboTax FAQ explains possible reasons why your return may be taking longer to get approved.