I'm not sure if this is relevant to you or if you're still bothered by this. Is the VN you are trying to save located in the external storage? Android 4.4+ has a permission where apps cannot write to the external storage of your device unless you give permission. Unfortunately, as RLVM hasn't been updated since 2014, the app doesn't ask for permission to write to the external storage and so it can't save the games.
If you put the game on your internal storage however, you should be able to save the game.
I had the same problem, I had Clannad on the external storage of my asus tablet running Android 5.0 and it wouldn't save, but I moved it to my internal storage and it worked.
I can see the biggest issue here being that a lot of phones and tablets don't have enough internal storage.
I hope this helped (if you are still stuck).
