I do what AmazingRando24 mentioned to “lock” posters if I’m being particular about it (sometimes I don’t really worry about it for some movies) and it works pretty well. Lots of folks seeing changes recently due to the default poster provider changing at Plex but so far, after going through and updating the ones that changed from that it’s stayed on the one I picked through multiple refreshes.
When I want a default poster to stick, I’ll pick something else then go back to the default one. I don’t know if that’s all necessary really but it’s what I do (just going to the edit screen with the poster might be enough).
The way a poster can be dropped is if the source pulls it - like if TMDB gets a report on it.
If you really really don’t want posters to change you’ll have to use your own. I’ve never had one I uploaded myself change on me.
Using PlexDash on your phone can make it easy to update\fix artwork if you don’t want to get into the web interface. I do this if I notice a wrong poster\background while browsing via TV. https://www.plex.tv/plex-labs/