Since filing our GA 2018 state income tax in March 2019 we have still not received our ~ $1,200.00 refund. Why?

Only the state can tell you.  Check for a state refund     <a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund">https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund</a>

Was your state return Accepted?  You can check your efile status here     <a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/tax-tools/efile-status-lookup/">https://turbotax.intuit.com/tax-tools/efile-status-lookup/</a>

When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc.  what does it say?

Per GA, allow 90 business days, which is approx. 4 calendar months.