Poor you and poor DS.
I would imagine he is reinfecting due to the lack of ability to fight anything, largely brought on by the antibiotics sadly! They can ruin the gut and hence the immune system although I know they are a necessary evil most of the time with infections, especially where tonsillitis is concerned.
We had this with DD, 6 sets of antibs last year between Sept - Xmas. My DD is allergic to penicillin so they always gave a real broad spectrum drug that did not touch her. I was concerned that the dose was never high enough (always 2.5ml x 4 times per day), we saw a consultant paediatrition at an emergency out of hours place when DD had been sick for days and she prescribed 5ml x 4 times a day. It did work at the higher strength.
I posted and was given the very best advice. I was told that once the course of antibs was over to give probiotics every day for a month. Not the yogurt stuff but really good quality powder form. I used acidophilus and it worked brilliantly. I also gave Dalivit for the rest of the winter which is a vitamin B complex especially for immune systems. It is really important that you rebuild the gut as soon as possible after the medication is finished, apparently you should not give probiotics at the same time as antibiotics as they fight one another. You can get the powder probiotics in good heath food shops, get the ones that have been refrigerated. They dissolve in drinks and either have no taste or strawberry flavor.
On a more practical level, have you changed his toothbrush? Reinfection rates from toothbrushes is alarmingly high.
As for giving the meds, well, that is the tricky one. We use a nurofen syringe and DD is allowed to do it herself, she finds this a real motivator.
Also, I give one chocolate button and on the basis one button is never enough I have the other two in my hand for after the meds. However, if he is not eating at all that may not be a motivator. Does he respond to sticker rewards yet? Or maybe put a DVD on and let him watch it whilst you pop the meds in?
DD is on antibis this week for an ear infection after 4 days in the pool at CenterParcs (not surprising!) and I will be giving the probiotics right after this course is finished.
Good luck, I am sure this will help to stop the reinfection if you can get him strong enough to fight it.