It does not appear that playing a card from your draw deck currently causes the deck to be re-shuffled:
Per the Comprehensive Rule Document 4.0: draw deck
Some cards allow you to play a card directly from your draw deck. You must still pay any costs and meet requirements necessary for playing that card. When you finish looking through it, reshuffle it and give the player to your right the opportunity to cut it. There is no penalty if you don't find (or choose not to play) a card you are looking for in your draw deck.
It appears that the only time the draw deck is shuffled is when you don't find the card you were looking for:
From the ChooseAndPlayCardFromDeckEffect.java routine
@Override
public void playEffect(final LotroGame game) {
if (isPlayableInFull(game)) {
Collection<PhysicalCard> deck = Filters.filter(game.getGameState().getDeck(_playerId), game.getGameState(), game.getModifiersQuerying(), Filters.and(_filter, Filters.playable(game, _twilightModifier)));
game.getUserFeedback().sendAwaitingDecision(_playerId,
new ArbitraryCardsSelectionDecision(1, "Choose a card to play", new LinkedList<PhysicalCard>(deck), 0, 1) {
@Override
public void decisionMade(String result) throws DecisionResultInvalidException {
List<PhysicalCard> selectedCards = getSelectedCardsByResponse(result);
if (selectedCards.size() > 0) {
final PhysicalCard selectedCard = selectedCards.get(0);
cardSelectedToPlay(game, selectedCard);
} else {
game.getGameState().sendMessage(_playerId + " shuffles his or her deck");
game.getGameState().shuffleDeck(_playerId);
}
}
});
}
}