No offense, but it is as though you didn't read anything I said.
To repeat and to explain: I don't know specifically what PKHeX checks for every save. (every as in the different games throughout the years)
I just know that it is usually a combination of these things:
1. Get starter
2. Access Pokemon Boxes
3. Saving twice.
Is that good enough? With that info, try to run a test with a duplicate save. If you don't run the test, don't provide a save, there isn't nothing much I can help you.
For all I know, your issue is something else. Once again, can't help you until you actually run the test and pass the save over.
I hope you understand where I'm coming from. I can't perform magic. I can only give my best guess based on info you provided, and you did not provide a lot.
Edit: As an addendum, if you're running some kind of Randomizer or ROM hack, PKHeX may not work anyway. PKHeX is meant for unmodified official games.