Keep him warm at all times and give him as much love and time as you can. They say vitamin C is good for the immune system, but I don't know how hedgehogs process it. I'd feed him mealworms or crickets that ate pepper and carrot, this way he might get access to some vitamins

I read every now and then that parents often don't let the hedgehog owner to the vet... just how much might a treatment cost, if I may ask? I've only taken my hedgehog to a regular check-up before because he's only 10 months old, it cost me 40 Euros here in Germany.
Edit: you are saying he's syringe fed though, so insects aren't an option, I guess?

Although if you don't find it too morbid, one could make like an "insect porridge" from frozen insects that were grown on vegetables? I am not a fan of feeding veggies directly, but I heard that cooked carrot and some apple does not hurt their stomach and they can be made soft

I'd try to convince my parents to take him to the vet at least once more. Hedgies might even live 7 years when well taken care of. Wishing all the best to you and your little one!!