The problem is the cheap-ass hinges and construction of Airstream trailers.
Our ultimate solution was to get rid of the Airsteam and buy a different brand of RV, made by a more quality and customer oriented company.
There are a number of similarly cheaply constructed items in Airstreams that the company management knows full well are long standing problems but they have their head so far into the sand that the'll never make simple fixes -- you know when you've been making these mistakes for so long, why change? (Leaking showers are another similar example that they refuse fix.)
We had continual problems with the drawers falling out in our Airstream - particularly the one in our bedroom vanity that faced forward between our twin beds. We took it back to the factory for repairs a couple times to no avail (and, no it wasn't coming out becasue our running gear needed balancing) -- it was due to those cheap drawer slides used by Airstream.
At one point, we had to take the drawer out and lay it on the floor when we traveled. However, our eventual solution was to put a velcro strap around it. I put pieces of velcro, attached with adhesive, on either side ot the vanity that were hidden by the bed mattresses, and then we attached the strap whenever we traveled.
We also used another velcro strap through the handles of several of the cabinet drawers in our kitchen.
You could also permanently screw the drawers shut -- just get a few of those loose screws that have been rattling around in the heads of a number of Airstream's management.