I'm not sure there is a limit... My base game (of an unsupported system) that I copy when I start a new campaign has over 1400 archived handouts plus the ones actually visible in the folder tree. Are you using any api scripts that interact with handouts? I'm not sure what else to suggest trying... You might try making a copy of the problem game and see if the behavior is different in the copy. If that doesn't work, then you should probably submit a ticket through the Help Center ("Send a Request" in the upper right corner) with all this info and the name of the game affected. Hopefully there is something they can straighten out on the back end.