How can I keep the aphids off of my green bell pepper plants?

I got my mom a grow box for Mother's Day and we planted one tomato plant and four green bell pepper plants. Our town home backs up to a woodsy/swampy area and there is any number of raccoonss, birds, squirrels, mice, etc. back there not to mention the bugs. So we keep the grow box on our screened in lanai. Everything did really well for the first few weeks, but in the last couple of weeks the green bell peppers have had white fies and aphids. We've tried two different insecticides and lately dish soap. We spray them in the evening and by the next evening there are new aphids, I cannot get rid of these little suckers!! The tomato does not seem to have any bugs, in fact there is even a tomato. I'm getting worried about the peppers though, all of the buds have shriveled up and died and the leaves are not looking so good either. We live in the Tampa Bay area in Florida so it gets very hot, I'm worried that what we spray forms a residue and then bakes on the leaves. Should I rinse the plants after I spray them? Any suggestions would be welcome!