Can you give your soapy home brew recipe please? I've tried blasting with water, and the tomato leaf extract deal and neither seem to help for more than a day or two.
Sure, what I use is no secret and to be honest I'm constantly experimenting with the ratios by increasing the amount of soap or peppers used. Just make sure to mist within 15 minutes so the leaves don't get burned. I do this process once every two weeks or once a month as needed. I also run this through the soil if I suspect any nematodes or bugs under the soil and it drives them out.
I keep a few empty gallon jugs that I chop up around 6 or more pods per jug (the fuggly/imperfect ones), I leave them this way till I need a new mix and refill them once empty. With this water strained, I mix in 1 oz. of dish soap per gallon of water right in the spray bottle and spray the bottom of my leaves, wait 15 minutes and I mist off the soapy water. Sometimes I mix them much stronger but be careful as the soapy water can damage your plants if you leave it on too long, oh and I do this process just before sunset or early before full sun. That said if you want to experiment with weaker mixing and leaving on the soap as I've read before I would recommend testing on your worst plant as I've never found a way to leave this on and not damage the leaves.
On another note, you say that you see pests again within a day or two, what kind of pests? If it's aphids, check for ants and you'll have to get rid of them, as they will constantly try to plant them under your leaves. I've yet to battle mites on mine but I think the soapy water should kill them, good luck ...
Edit: 2 points, as romy6 said “we encounter more than most is bugs,” so keep an eye on them. And if you are experimenting with different ratios, I would keep a test plant that you don’t mind it dying if the test goes wrong. One year I had some nematodes in a potted plant and I went as far as soaking the whole pot in a large bucket of chlorinated water. While that worked, I’ve found my soapy solution is better as I can leave that in the soil and it keeps them away for good. I’m still not sure how they get in there but from what I’ve read they seem to be everywhere in FL :/