I respect that you dont want to talk too much about his particular circumstances. So in saying what I am about to say, I might be talking aloud out into the dark, but please bear with me.
If there is any chance that he has iron deficiency, there is no harm in giving him vitamin supplements with iron as a stop gap measure. It could also be an idea to monitor what he is eating, if he is not eating enough red meat, or green leafy vegetables, eggs, or other sources of iron, such as baked beans, marmite, red currants, black currants (fresh, not ribena )etc, it might work well to include these, and make sure to not give together with milk as milk hinders the absorbtion of iron to his body, while orange juice (vitamin c) helps the body absorb iron.
I was going back and forth between gp, consultans, for nearly two years. It was incredibly frustrating. I kept saying "he is ill, he isnt eating, he has no energy" they found nothing wrong. They said, he is a typical fuzzy eater, no need to worry. Well, for me it was a need to worry. When you have aenmia, you lose your apetite and your energy. So, it didnt matter how much great food I tried to make him eat, he just wouldnt, he had no apetite. It took a long while to get his iron levels up. But slowly but surely his energy levels have increased so much. He has gone from sitting on the floor looking at a puzzle, or mooching infront of the tv, not wanting to play out and do physical activities, frequent napping, starting out eagerly in the morning, run down the stairs, just to sit down and say "please carry me" to be bouncing about like the duracell rabbit.
He did have something else though, that contributed to his lack of apetite, as he also had a long slow build up to appendicitis. He has also had a tonsillectomy. Due to his low iron levels, his immunesystem was pretty bad, and he was having tonsillitis once a month. He had his tonsils out in February, so it has been 9 months now without tonsillitis (touch wood).
I think, with aenemia, children are prone to other illnesses, be they viral or bacterial and this tap their already low resources even further.
As a mum, you KNOW they are unwell, you just cant prove it. My son was tested for all sorts of disorders, including coelic disease.
Sorry for my long post. What I am trying to advice, and sorry if I overstep the line, is to maybe tailor his meals to include iron rich foods and vitamin and iron supplements "just in case". Unless you are doing this already. Good Luck.