Frontier Airlines flies the Austin / Denver route non-stop, and is selling one-way tickets for as low as $29 for August and September travel.
https://booking.flyfrontier.com/Flight/Select
The above link should take you to Calendar View, which will show you many available dates for this low low fare.
If you want to avoid the fees that Frontier charges, you can fly on Southwest for just $117 r/t or United for $133 r/t.
Nonstop Flights: Austin to/from Denver $117 r/t – United / Southwest