I don't think it was explained in the series but one of the things most people assume is that Menma returns because she wants her wish fulfilled. This, in turn, could mean that once her wish is fulfilled, she leaves. So the assumption is that she disappears because her wish was fulfilled, but what if her return didn't have anything to do with her wish (or specifically here, the "make Jinta cry since his mother thinks he shouldn’t hold back anymore"). So it's possible either she has returned for some reason unrelated to her wish or she lied about what her wish actually was. Note that these two things are not mutually exclusive.
So the scenarios here are:
Menma lied about her wish, and she returned to have her wish fulfilled and at the end, it was fulfilled and she disappeared. All this time, the audience (and the rest of the cast) doesn't know what the wish is and thus don't know why she returned and why she disappeared.
Menma's wish was actually to make Jintan cry, but that's not why she returned. Thus perhaps even fulfilling the Jintan-cry-wish, she doesn't disappear because the reason for her return is something else, which was completed at the end of the series.
Menma's lied about her wish, but her return was irrelevant to that wish to begin with, leaving her disappearance a mystery. It's possible in this scenario, that the wish facilitated whatever it was that allowed her to leave.
As for what the wish was and why she left, it's probably all speculation. There's a blogpost that speculates about the possibilities of Menma's wish and her reasons for returning. Note that this was written before the ending of the series, but if we are to assume that the final wish (or the reason she came back) isn't what she claims, then a lot of it is still applicable.
It's completely reasonable to assume that the extension of her wish was meant for "Jintan to generally open himself up again to different emotions like enjoying himself with his friends, to laugh when he's happy, to get angry when he is, to cry when he's lonely", and the entire journey of finding what it was the Menma had originally wished for accomplished this. And that sort of mean her original wish wasn't what brought her back and not why she left at the end.
As for how she planned on accomplishing her original wish if she had not died, I don't know.