Alyssa, the soap is very effective. You don't need something stronger to kill off your thrips. Stronger is not necessarily faster or more effective, but is usually much more toxic.
The reason you need to keep repeating the soap application is because it will kill off the bugs that are present, but not the ones still in their eggs. To get all the generations, you probably need to spray everything with the soap about twice a week for a couple of weeks. Be sure to get the undersides of the leaves, the soil surface, and all around the pot as well.
