I am actually struggling with a similar issue which I will explain after commenting. The reason I mention it first, though is because it is that issue which gives me a sort of different perspective on this situation.
I think that the reciprocity issue is sort of a red herring. Or maybe not a red herring but a symptom of a larger issue.
The real question, in my mind, comes down to whether the OP's mom really wants to invite these people to her party. Regardless of the reason why not, if she doesn't want to, then she shouldn't. Maybe the reason is that she has no contact with them the rest of the year. Maybe it's because they really aren't her friends but her friend's friends. Or... maybe it's because she doesn't like them. Or because they always bring blueberry pie and she doesn't like blueberry pie. Or whatever!
The bottom line is that it's her party and she should invite those people who she wants to invite. Period. Her own private reason why someone who got invited in the past is not getting invited this time is just that: private.
Now, of course, that doesn't mean there won't be fallout to deal with. Especially when it comes to the neighbors and the hairdresser. So then it comes to weighing the consequences of not inviting them vs. going ahead and including them. But that is still her decision regardless of her reasons.
So here's my similar dilemma. I have an annual party which I've been doing for more than 20 years. This party entails effort on the part of the guests, both before and during, in order to be successful. Not everyone participates in this effort, which is fine because there are always enough people who do to make it a success. There are some people who I have invited for years, who always come and who participate fully, who, and here's my problem, I just am not wild about anymore. Maybe they've changed, maybe I have. Maybe just over the years certain aspects of their personality have grown old, I dunno. But to put it bluntly, I don't really like them anymore.
I have agonized repeatedly about taking them off my list. But the thing is, they come. Pretty much every year. And the participate. Fully. Lending to the success of the party. I feel bad scratching them off the list.
My reasoning above for the OP's mom really comes into play here. I don't want to invite these people, yet I continue to do so. It shouldn't matter why I don't want to invite them, nor should it matter what their behavior is (in OP's case, negative by not reciprocating, in my case, positive by fully participating). It should just come down to one simple question: Do I want them at my party or not?
Does your mother want them at her party or not?
Again, I realize that it's more complicated than that, as I've noted that although I feel that it should be that simple, I recognize that it's not based on my own situation. But maybe it will help your mother to at least look at it that way for a moment. Because sometimes, the simple question and answer can make it easier to drop the extraneous stuff and see it for what it really is.