How to make "Get Mail" button work for new IMAP acct?

Question

Recently, I started new Internet service with Charter. I set up my new email mail account on my iMac, and everything is working perfectly.....except that Mail checks the Charter email account for new messages ONLY when Mail is first started or the first time I "Synchronize". There's no way to know that messages are waiting, and no other way to download messages.
When I click the "get mail" button, the little wheel thing appears for all the accounts (I still have my ATT accounts active), except the Charter account. When Mail automatically checks for messages, it checks all the accounts except the Charter account.
The messages sent to the Charter account show up right away on the web (looking at my account on Charter's web site). I have no trouble at all sending emails. I have the account set up with IMAP (although, I tried POP, with no change). I have this account set to "Include when automatically checking for messages". I've shut down and restarted multiple times.
I've talked with Charter support, and they've checked their server and all my settings, and everything is OK. I'm inclined to agree it's not an issue on their end. It seems to be Mail.
Any ideas on how to fix this?

Answer 1

Yup. It was set to "every 5 minutes", and changing that made no difference. Mail completely ignores the charter account when doing the automated mail check and when I click "get mail".
I went to the local Apple store, without my iMac but with screen shots of the email settings, plus settings info from charter, and we set up the account on one of the iMacs there. It worked perfectly. The guy helping me suggested deleteting the account and setting it up again.
I did exactly that, but the behavior is the same. So.....the next thing to do is take the iMac in. (sigh.)