So let's talk about abilities for a second.
In e13, when a Pokemon was created, it's ability ID could be 0, 1, or 2, because HAs were available in the wild.
In e14, the code was changed so that an ID of "2" was unavailable for a lot of these wild Pokemon, so some got changed to the ability represented by the IDs of 0 or 1. This meant some wild HAs would swap to be non-HAs.
I wasn't sure if I could fix it and offered the immediate solution of ability capsules, seeing as their availability is "effectively infinite." If you took this route, you have changed your Pokemon's internal ability ID, and whatever ability you have should be the one you've got. I know the e13 and earlier capsules were messy but I'm pretty sure the e14 capsules are a clean enough implementation that your changes should be preserved. (Keyword should.)
For e14.1 I have fixed the issue stopping 3 ability Pokemon from having their HA in the wild. I think (some) Pokemon's abilities will shift again, but I'm not 100% sure and haven't done extensive enough testing to find out. Pokemon who've had their ability changed with the capsules should stay as whatever they're at but I'm not 100% on that either.