You don't want a real tight seal, and air it out daily, keep the cup on a little less each day and when the heat does not run much I think you will not need it at all in your climate.. A clear tub would be a good investment and it keeps things neat.
I think another thing that might have made a difference is that alot of the cutting is above the soil line. When it is in a box of sphagnum moss it can absorb water through its entire length through the bark. But now the top is drawing water and it has become imbalanced because the roots are not ready to take up enough water yet. I am not sure exactly when roots begin to absorb water but I think it really increases as the roots branch and their surface area increases, which takes a week or 2 at least.