It's always hard to know why a plant isn't doing well, especially without seeing it, but the most likely explanation is that your Ilex vomitoria (Yaupon) is suffering from transplant shock. Even under the best circumstances a plant will suffer some degree of setback when it is transplanted. When the transplant is done in the spring, the shock is exacerbated by the stress of hot weather soon after being planted. This is why Mr. Smarty Plants always recommends planting trees and shrubs in the fall.
At this point, about all you can do is make sure it is getting enough water. A yaupon doesn't require much water after it is established, but it will need some extra water to get established. Be careful not to over water though, yaupons don't like wet feet. A layer of mulch arond the base will help.
Mr. Smarty Plants can't tell you if your plant is going to die or not, but you will probably know the answer by this fall which will be a good time to plant a replacement if it doesn't make it.
Here area couple of how-to articles that might help you out if you have to replant: