tagged photos not staying tagged

What kind of tags have you been adding? Have you added captions or places or named the faces?

The face names may have to be added again, whenever the algorithm for face detection has been improved by a software update. ThenPhotos will frequently scan all photos again for faces, and if a face has been detected in a slightly different location, you may need to confirm the name.

Did you perhaps install a system update previously?

Another possible reason for vanishing face names might be, that your photos have been synced from a computer to the iPhone. When you sync again, the previously synced photos will be replaced by the most recently synced photos, and then you have to add the tags again.

You mention your Mac, but you don't say-- are you using iCloud Photos to synchronize pictures on your iPhone and on your Mac? If so, then why not use the Mac for naming faces? It is so so so much easier and more versatile than the phone for this. And backups are easier.

On the other hand, if you use a cable to transfer pictures from the phone to the Mac, then, as léonie said, this process replaces pictures, and it may cause changes you've made to be replaced, as well. I haven't used this cable transfer in years, but my memory is that things get added to the Mac though never added to the iPhone--but things can get subtracted from the phone.

if you are syncing photos manually from a Mac it is a waste of time to tag them on your iPhone. The synced photos are in a lesser quality than the originals on your Mac and a new sync will replace the previously synced photos and any work you invested into them. I am only syncing with iCloud Photos and tagging the faces on my Mac, like Richard recommended - it is easier to avoid tagging errors on a Mac.