Without losing player to player interaction. What if they had a market for items people were selling and are only available if they (the player selling) are online.
Say youre MR 20 so you can only display say 10 items that you want to sell on a market, but don't have to just sit on trade chat and wait for someone to buy. You can keep playing the game. People can see your items that you have listed up for sale, almost like on Maroo Bazaar. But once you go offline, those items aren't available. And the interested party can just PM you for their interest in that item and you all can negotiate from there and meet up and trade like normal. Who enjoys sitting in trade chat and not playing this game? I understand what an AH would do to the game (dillute the price of things, everyone would be selling at all times and drive prices down, lower prices and more competition would mean less plat would need to be earned or bought for a particular item, less reason for people to spend more on plat and less profit to DE, and the player to player interaction wouldnt be there anymore)
So it wouldn't be an AH where you place an item up for sale and someone just buys it while your playing or sleeping, or just doing whatever outside the game. You would still have to go and trade with that person, and negotiate etc. So basically it would just be an advertisement for what you are selling. They still have to come to you for the item they want to buy. That's my thought on this issue.