Update: After quitting and reloading the iCue software a couple of times, it displayed a message saying that it needed to load the onboard profiles. I told it to do so, and now the profiles are loading and saving in iCue. However, it also did this right after the update, and the next day the profiles were missing and it didn't prompt to reload when the software loads with Windows.
So, with that, I can only assume that there's a bit of a bug in the iCue software update that allows it to forget loaded profiles.