Icons opacity or groups opacity? Easier for groups because it's a simple slider to add, but for icons (individually) it requires a bit of code reforming.
I tested it and you're right. I checked the whole code where it handles duplicating and moving and seriously I didn't find a single line that links the duplicate to the original, so I think it a problem with how the game handles the frames or new created frames or something. I will loot into that more and see if it's me being blond and not finding the issue or it's really a game-related problem. Thanks for reporting it though.
Tip: No need to relog, after you duplicate a group and do your modifications (without moving), just do /reload without locking/unlocking, that should fix the issue, at list for now.