So it looks like I've solved the problem. When I was at work earlier, instead of working on my game like I wanted to, I downloaded the update. It took about an hour on their horrible wifi, but I got it done. Since I didn't have time to do anything else, I decided to test a theory of mine. I went into offline mode before shutting down my computer. After work while on the bus, I turned on my laptop and started Steam in offline mode. I was able to run all of the capx files that required the updates, which meant that the update was finally remembered.
It's another inconvenience of DRM, which I should have expected from Steam. You have to be online to go offline (go figure), or it will roll back your updates until you're online again to update again. Without turning this into a debate about the ridiculousness of DRM and how it punishes real purchasers of software, I must say that I am relieved to know that I can use Construct 2 at work now.