Only the state tax agency will know what all it is doing with your return.  Virginia can take up to four weeks or so to process e-filed tax returns and 8 weeks for paper-filed.

First, use this tool to doublecheck that the state return was successfully efiled and accepted:
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp

If accepted, or if you mailed the return, here's how to track it:

FAQ: How do I track my state refund?

https://ttlc.intuit.com/replies/3300211