It turns out that this, in combination with the more or less standard box spring that they put the mattress on, leads to a nasty little design defect. If you sit down on the edge of the bed to, say, put on your shoes and you linger a bit too long, the bed will deflate beneath you. This would not be a problem, except that the box spring edge is simply a long thin metal rod. Normally, the box spring can take a fair amount of weight, because the mattress is distributing it across the entire unit. But when the mattress deflates, you are now sitting on directly on the unprotected rod.
The rod is not actually expected to bear weight in this fashion and it doesn't. It bends.
So now you have a box spring which is not so much straight as concave. Concaved in, to be exact.
We had one unit fail in this fashion and got it replaced. Now a second unit has failed in the same way. This is not good. The replacement is on its way, but we have to do something about the design problem.
The solution is to find a way to prevent all of the weight from ending up on one spot, even if the mattress deflates. And reading through the discussion of these beds on the Internet, one thing that was suggested if you find that the box spring is giving insufficient support is to put a piece of plywood under the mattress. Well, our problem isn't insufficient support, but a piece of plywood is stable enough to continue to distribute weight across the entire box spring assembly.
So last night, Sam and Bonnie came over. One trip to the hardware store later, we had two cut-down pieces of plywood, which we then took into the garage and trimmed to fit the various cutouts on the box spring. They are now installed under the mattress -- and the ones on the damaged box spring are being stuffed with old sheets to provide support along the concave edge.
The mattress is now *quite* firm. And with luck, the next box spring will be a survivor -- with many thanks to Sam for all of his help.