I've already covered parts of this as part of the "under-eating in children" section of How the Whole Asperger's thing can be detrimental to your Health but now it's time for more detail and a few real-world examples.
Why don't aspie children eat?
Texture plays a very important in aspie eating habits. For example, I have problems eating peaches because of the feel of their skin and because of the "powdery" taste of the fruit within. I also have a lot of problems relating to sultanas which I believe began with texture issues. For a long time I could eat sultanas in biscuits because they were dried out but not when they were in cakes. now I can't eat them no matter where they are.
Possible Solution: if you have a texture issue, you can get around it by mashing or blending the ingredients. Just make sure that there is no skin left on the object before you serve it. If the child still refuses to eat/drink the substance (without knowing what the ingredients are) then you probably have an issue that isn't texture based - it may be taste.
The role of memory in aspie eating habits is very underestimated. This is mainly because very few aspie children communicate about the problems and it tends to lessen as you approach adulthood. I guess that probably the best rule to give you is to never feed an aspie child while they are under stress. Of course, this assumes that you have any idea that they are actually under stress.
I remember having lunch with my family as a child. I'd just had a pretty bad argument with my father at the time and was sitting at the table somewhat "steaming". My mother served us in a piecemeal lunch consisting of various slices of fruit and veg which included slices of banana. I was so angry with my father at the time that I was refusing to look at his face. I ended up staring at his shirt instead. It was then that I started to realize just how much a sliced banana looked like the buttons on a shirt.
I was still pretty angry with my father the following day and my mother served up pretty much the same lunch again. This reinforced the buttons to bananas link and pushed it into long-term memory. I also got into trouble for refusing to eat my bananas.
The long term effect of this was that I went off bananas for about 10+ years. I also had problems touching the buttons on my shirts for that period. Actually, I still have some textural problems with buttons and there are some types of buttons with darkish - sort of bruised fruit patterns in them, (I call them "tiger buttons" because they're a bit stripey) that I still can't even look at.
When aspies focus on their special interests or when they're out playing they can often completely lose track of time - and forget to eat. I still have this problem at work and it's quite embarrassing because I'll often have guests in for a meeting and will forget to feed them or offer them drinks.
At school, distraction is a big problem because during lunch time, the aspie child is trying to cope with a huge amount of multi-directional stimuli. Remember that aspie children are often more distracted than NT children.
Some schools, including the one that my son goes to, make sure that the child brings home every bit of lunch that they don't eat. The aim of this is to make parents responsible for providing the child with food that they enjoy eating. What this doesn't address is the fact that the aspie child probably does like the food but is way too busy to eat it or even to remember that it is in their lunch box (or on their lap).
I've seen this effect with my kids when I let them eat while watching TV - the food is right in front of them and they can smell it. They're hungry and it's food that they like. The problem is that the TV creates so much distraction that the child won't remember to eat without constant prompting.
Since there is no constant prompting at school - the school lunches just aren't going to be eaten.
Possible Solution: Give the child a token food to get the teachers off your back. The food should be something that is wrapped and won't go off after a few days (like a muesli bar). You should also give them some money in case they get hungry while at school - that way they can buy some lunch if necessary.
Feed them as soon as they get home - lunch food at 4pm, not dinner food. Don't worry too much about spoiling their dinner, but keep the after school food fairly healthy and reduce the amount you give them for dinner.
It's actually healthier to eat big breakfasts and small dinners anyway though it's not considered too healthy to skip lunch - we're not skipping it anyway, just postponing it a bit.
If you try to force your child to eat their school lunch, they will just be forced to find more creative ways of getting rid of it. I remember being at school and being very selective about where I sat. I always sat on the balcony above the rubbish bin. This gave me the perfect opportunity to discreetly drop my sandwiches off the balcony. The only time I got caught was when moved the bin during lunchtime and found the ones I had missed lying behind it - still wrapped up.
I'm a little skeptical of this but there have been a lot of studies that show that medications such as Ritalin do suppress appetite. The reason I am so skeptical of this is because aspies are well known as picky eaters and Ritalin is not technically an Asperger's drug. I'm not sure how reliable the control groups used in the research are.
Nevertheless, if you have your children on any medication, make sure that you take notes before and after (on and off) medication - and make sure that their weight is checked regularly by your paediatrician.
Most people have one or two foods which they don't enjoy the taste of. I've not seen this as a specific aspie thing. If your child doesn't like the taste of a particular food, there's nothing you can do. Find an alternative food.