I think my parsley plant is dying. It started out strong, however now it looks wilted and falling over. Is there chance it will be ok?

Looks a little shabby but nothing it can't bounce back from.
Can you give us a patient history? Watering schedule, how much sun it gets, whether you've done anything different with it recently?

Sure, I have been watering it every other day. I would say it gets about 5hrs of full sunlight a day. Then it is moved to the shade. About a week ago I did try using a vegetable and herb fertilizer that was recommended to me. Dr.Earth Home Grown Organic Pump and Grow. I used 1 pump since it is in a small pot. I wasn't sure if the Tx heat was playing a factor.

Heat could be an issue, but you're doing the right thing with shading it partially. The soil in the picture looks somewhat damp - like it was watered recently, not like it needs to be watered again.

Someone suggested elsewhere that shading the pots to keep the soil cooler even when the plant tops are in the sun can help when growing in containers. I am not a container expert, but that seems like a good idea with something like parsely that doesn't like the heat so much. A larger pot would also help keep the soil cool.