I did some more testing and it seems the cause is not that a card keeps the pig picture over several turns until it reaches the hand again. In the game mentioned at the start of this thread, an Emporium has a pig picture, but an Emporium was never effected by Enchantress before!
The turn in question (15) starts with Accatitippi drawing 4 cards at the beginning of the turn (2x Hireling, 1x Enchantress), among them an Emporium. He already had an Emporium in hand. He then played *another* card (Menagerie) under the effect of opponent's Enchantress. This seems to be the crucial circumstance, which I could reproduce in another game. In this case, the last Emporium still has the pig picture.
The problem seems to originate around the start of turn. If one undoes to the first decision in that turn (after the start-of-turn effects, before the playing of Menagerie) and then replays the turn exactly as it happened, the last Emporium will *not* show the pig picture. If, however, one undoes to the last decision of opponent's turn (buying a Silver), and again plays out turn 15 as it happened, the last Emporium *will* show a pig picture.
My guess is that some bookkeeping about which cards and how many of them need to be 'pigified' happens when the turn starts (before any effects happen), but that this info isn't updated when more cards are drawn.