I know everyone is being nice but does anyone think it might be the ASD?
It's not as simple as saying "it is / is not the ASC". It's extra easy for children with social disabilities to drop below the invitations radar and it's extra hard for them to climb back up again. They have all the usual reasons for missing invitations and on top of that they also have reasons related to their disability. And some of those extra reasons happen to kids whose behaviour is fine.
To cope with the social demands of school a lot of kids with ASCs need extra chill time alone after school, and many others cope better with regular and structured activities out of school (which is what the OP's DS does). So even though they have good friends in school who play well together they still can't be part of a group who casually play round of each other's houses after school.
But that doesn't make the school-time friendships and the parties any less important, if anything it makes them more important. Only it's easy for kids to get dropped from invitations as friendships change and parents don't see them around.
surely he is in and out of their houses, doing playdates etc at yours etc.
I've met quite a lot of primary-age kids with ASCs and I can think of exactly one who could do that.
your definition of close friends and theirs might not be the same.
Well yes, it might not be the same, and that's one of the problems our kids face. Other parents don't know how friendships work for kids with ASCs.
I kept up DS' big birthday party even in years when he got almost no return invitations. It was what he wanted and made his birthday special like any other kid; it kept him in the social swing a bit more than he would otherwise; the other kids could have a good time without feeling over-burdened; and it probably did get him one or two extra invitations over several years. (And actually my DS had behaviour problems which did limit who invited him back and I have no complaints about that.)
Anyway, this is part of the reason I agree with the OP that she should simply keep quiet and invite the other boy. The boys get on well enough and asking isn't likely to get a useful answer. The important thing (to my mind) is to invite the other boy to keep the social channel open. And maybe if you get a chance OP, to mention to the other mother that your DS values his friendship with hers even though your DS doesn't get to spend much time with him. (But only if you feel like - you might prefer to save it for one of the nicer mums.)