We're doing pretty well here atm with food. When J was a baby (he's 9 now, has AS) he ate everything that was put in front of him but this changed almost overnight with a certain controversial vaccination... For the next six months avocados and bread were pretty much all he ate, plus the occasional yogurt. Somehow he started eating again but until he was about four everything was beige - potato products, chicken nuggets (I think he got into those from kids parties), bread and beans. He had an extremely limited range.
At four I realised he was never going to come out of this on his own so I started teaching him how to eat. I'd sit with him for ages at the table, putting a sliver of a new food into his mouth and following it quickly with a baked bean or something acceptable. There was a lot of upset and tears and I hated doing it, it felt cruel to force him, but now looking back I'm glad I persevered because he now has an excellent diet and is very healthy, and actually enjoys his food. Gradually he got onto real meat and vegetables, but in true aspie fashion there were no combined foods and nothing was allowed to touch. He actually had a good diet but nothing that anyone else would eat. It took years to reach the stage he's at now and is still very much a work in progress.
He had a year on the gluten free diet and because he was keen to try that in the hope that his behaviour would improve, he was more interested in trying new foods but still his range was very small.
Recently I've been trying to extend his diet to more social foods, essentially the stuff that kids usually eat. We've done this with a range of charts and achievement awards for each level. He starts off just discussing the new food, then works on tolerating it on his plate, then a touch or a lick etc etc until eventually he can accept eating it. It's an extremely slow and laborious process, certainly nothing is guaranteed, but he's coming on and will eat sandwiches now, which would have been out of the question a few months ago.
A huge achievement came at the weekend when we played a game of pretending to be herbivorous dinosaurs, foraging for food. I laid out plates of lettuce, rocket, cucumber, celery etc (all green) and we had to fight each other off to get to the best foods. J loved it because he got to eat off the floor, using only his teeth (he also enjoyed pretending to crap in my den but that's another story). Essentially, at this point he's overcome his fear of trying new foods, which is a massive landmark for him.
I really do believe that children with SN can be taught to eat but it takes an inhuman level of time and effort and it's probably not possible if you have more than one child. I've seen us lose whole days to the subject of food (not that I'd be spending that long forcing him to eat bananas, you understand!) and you can't do that with other people's needs to attend to. I fully agree with those of you who say you're happy just as long as your child is eating and getting some form of nutrition because that's where we were for many years. I'm just lucky that I don't work and have only one child so can spend hours and hours on this, but it certainly hasn't come about naturally.