Hm, well it's not a problem with the phone since it works when done manually, so it's definitely something that's preventing the phone from auto-refreshing your e-mail. It's most likely a setting somewhere, though might not even be in one of the email apps, might be an app you updated from the market that changed it. Is mobile data enabled at the settings bar at the top when you pull down the notification menu??
I will say I've had nothing but problems with the Yahoo mail app when I've had it installed, and I'm not sure what a Charter PoP account is? Is that another PoP email program like outlook or something?? Outlook is also tricky. You probably have, but maybe try uninstalling both, resetting the phone, and reinstalling them.