Is someone trying to retract him? If he isn't fully retractable it should be left alone, if he is fully retractable it can still be left alone as it's self cleaning in children. Don't retract it at all, don't use soap or bubble bath, make sure he is wearing cotton undies double rinsed and once he is healthy just 'neglect it'. The foreskin is similar skin to the eyelids and usually the cause of infection in the eyes is from someone messing about with it and the foreskin is the same. If it gets pulled back and the area isn't retractable tiny tears can happen and if the person doing it has bacteria on their fingers it can get in and cause infection. The white stuff is probably just smegma also known as body soap, you leave that alone as well. I would tell your son to stop messing with it for awhile as little boys can have all kinds of stuff on their hands.
What were the symptoms of his balanitis? This is often diagnosed when the child doesn't actually have it.
When you used antibiotics, did the DR take a culture or just give you a broad spectrum antibiotic? Sometimes because they prescribed broad spectrum it looks better but after awhile it comes back again. Make sure a culture is taken.
After years of researching a healthy body & gut, I've determined that the genitals of males are just as susceptible to an imbalance of flora as are the genitals of females (years of yeast infections, I now know why). If you or your son have ever had antibiotics, either were born by cesarean section, were artificially fed, eat the standard american diet, are exposed to large amounts of toxins and/or any number of other factors that can impair the healthy function of the body, it's likely that the balance of normal bacteria & other organisms that are supposed to live in & on the body is off. If he doesn't already eat truly fermented foods and/or take a high quality probiotic, then this may help. Applying a probiotic topically may help as well. Making a paste of the probiotic & a little water will help spread it on w/o it just flying away. At the age of six, he can use an adult probiotic (our bacteria are meant to change at the normal age of weaning which is between 5-7 years).
I don't have much time so I can't explain further. If you'd like more info, you can search my username in this sub-forum as I've mentioned it before. You may also PM & I'll write back as soon as I can.
I do hope you find something that helps him to avoid this problem in the future. One other thought, you could contact Marilyn Milos of NoCirc (she's an RN) for her opinion as well.
Best wishes to you both,