I processed my federal tax return online and paid my Fed Return with CC on Turbo Tax website. I am now getting notice from the IRS saying that it was never paid, why?

What is the description on your credit card charge?  Maybe you just paid the Turbo Tax fees with a credit card.  Or you entered something wrong on your credit card and it didn't go though.  

Your only proof of payment is your bank statement or credit card showing the payment coming out.    And the IRS or state does not update Turbo Tax when or if they get your payment.