I took ds out of school at the beginning of Y5 when he was almost 10 so have been HEing for almost a year and a half. He has AS and our story was similar to yours - needs not being recognised (we tried two schools but there was no practial support at either) and little intervention from the LEA or the medical side.
The decision to deregister came when it became apparent that the school had their heads firmly in the sand and were never going to support him. Although he'd always had significant behaviour problems he'd somehow managed to stay ahead academically, but when they refused to acknowledge how this side of things was beginning to suffer we pulled him out without hesitation. By this time he was highly unstable and had regressed by 18 months in five weeks so I don't really think we had a choice - removing him was an act of child protection, to be honest.
HE is by no means an easy option but ds has flourished since being out of school. As ommmward has said, stress for such kids is huge and they struggle to learn when they're under such pressure all day. Nowadays, although he still needs a lot of support and 1-1 to get him through work, he is far more amenable and motivated and he very rarely loses his temper now. He's calmer and happier all round because he's not subjected to those constant demands that he's not equipped to cope with.
I don't know anyone with an AS child who has HEd then returned the child to school later, so can't help with that (agree - HE special is the place to go for that kind of advice). As for us, it's not my intention to send ds back because I honestly don't think there's a school in my area that will support him, regardless of policies and paper intentions. Too much of it relies on budget, IMO, rather than the actual needs of the individual child, so there are no guarantees. The only way my son will go back into school is if I can be sure he has developed his social skills sufficiently to be able to cope in that environment, but I'm not confident that that will be possible. I'm more holding out for him to go to college post-16 which I think will be more suitable for him personally.
Oh, and the statement thing... if your son doesn't have a statement at this point and you're applying for stat assessment, you'd go back to square one if you take him out of school. Most LEAs will say that the child has to do at least two rounds of SA+ before they can be considered for assessment, which in practice could mean two years without adequate support. That's not strictly legal - I have known families who have applied for and been granted statements while HEing, though it's not common and you'd have a heck of a fight on your hands if you were to go that route.
Good luck with your decision. I'd be happy to talk to you some more about this if you want, just let me know.