This happens to me ALL the time nowadays, and there are two different scenarios. I haven't noticed any particular course of actions that cause it, as far as I can tell it's random.
1. Characters are just flat-out missing from the screen. The game believes they don't exist, and the list is short (sometimes very very short, sometimes only 10-20 missing).
2. The UI obviously understands that the characters exist, but their node is missing. IE: Blitzcrank BLANK Caitlyn. You can't click it, and there is no image, just a blank spot where the champ picture/name should be.
Nothing seems to fix this except for waiting for a few minutes (I'm assuming so that some sort of memory purging happens), restarting, or playing a game.