I think 'the months following' should be accepted. This is a perfectly acceptable formation in English
I agree, as a native Philadelphian, we can say, for example, "Things dropped off in the months following," just as well as we can say, "Things dropped off in the following months." I think that it is implied that the "months following" are following something in particular (that is, the event that will already have been established by that point in the conversation).
We can quite happily say "The months following". We might say something like "He felt a little insecure in the months following, but ..." again, an acceptable English phrase is refused while some atrocious errors get through.
The months following mean the same thing. I know it's in the comments already. Please fix it.
Despite this only being three words, I never got it to understand me when I was speaking and had to skip it...