My son's eating is erratic but not as bad as your's. Still, we're pretty sure its related to a combination of things, not the least of which are digestion issues, which are quite common in AS. There are many times my son really can't eat, it just doesn't feel good to his stomach, and we do have constipation medicine we can give him (when he hits periods like that he usually agrees that it's time to go back to having his "drink of the day" which is the medicine). Remember that it is the long term patterns that count, not the short term, and avoid establishing bad food habits just to get him to eat. I do like the shakes, idea, however. There are lots of way to make really healthy and great tasting variations of a shake or smoothie.
Also, keep a diary noting foods eaten recently, other things going on with him, etc. This will help your doctor figure out if there is something that can be done medically to help.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).