I have this issue on both free and premium accounts, using windows PC or laptop. I change the playlist cover with a new one but for some reason Spotify reverts to the old one.
Thanks for searching for the answer you need here.
If your playlist cover is not updating we recommend that you first try logging out of your Spotify account, restarting your device and logging in anew.
If that doesn't do the trick, it's a good idea to run a clean reinstall to remove any possible damaged app files.
Keep in mind that it might take up to 48 hours for the cover art to get updated.
Hope this helps. Let us know how you get on.