It says my last year state was accepted. It's almost time to file next year's. My state website keeps showing no record. What is going on????

After completing the File section and e-filing your tax return you will receive two emails from TurboTax. The first email when your tax return was transmitted and the second email when the tax return has either been accepted or rejected.

Do you have a copy of the TurboTax email indicating the state tax return has been Accepted?

If so, you need contact your state agency for the status of your tax return and the state tax refund.

See this TurboTax support FAQ for state department of revenue contacts - https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-revenue/L9qVToi02_US_en_US?uid=lpfwa2zf

It is possible your state received it, accepted it, and then lost it.  Contact the state to see if you need to mail them a paper return.