Assuming it's not a glitch, the fix would be to do exactly what C2C said above. The key to remember is that both you and your trade partner must follow all of the transaction steps, in the order listed above. That means that if either one of you receives your package and immediately goes from "package sent" to "complete" it will not update the list.
I believe that when you mark a trade as "package received" it transfers the cards to your collection, so if that step is skipped (which I would guess is the most likely step to skip) it wouldn't move the cards.
That being said, if both you and your trade partner are following both of those steps and still having a problem, perhaps there is some sort of glitch there.
I'll never quit collecting entirely, but I am downsizing. Check out my COMC store and help me thin out what I don't want so I can buy cards that I do want. See something you like? Send me a message on here, and we can knock the price down quite a bit. I'll even take a bit of a loss if it means getting you a card you really want.