Somewhat to my surprise, I had a package from Dell on my doorstep yesterday evening -- the replacement wireless card. I transplanted it into the box that was having problems, and so far things look good. It reliably connects to the home network, and even if you leave it running for hours, it doesn't lose the connection the way it was before. So perhaps the problem was indeed in the wireless card. I'll send the old card back to Dell in the postage-paid return mailer on Monday when I get back from Oregon.