It turns out that my apps that were disappearing were installed on my SD card, without me even knowing or telling the apps to install there. Went into settings > Applications > Manage Applications > On SD Card to discover this. If you click on them, it gives you the option to Move to Phone.
Now my apps don't disappear. But it seems to me that if you have Apps installed on your SD card, they shouldn't just disappear from your home screens every time you mount the SD card to a computer. (And they disappear permanently, not just for the time that the SD card was mounted, because that would actually make sense) Seems like a flaw to me.
I guess it should be noted that I'm running stock Gingerbread (no root) update .588