In case anyone else runs across this, I thought I would document my findings here.

The CIM/WalletSelector code is wrapped in an update panel, which means that updates to that control aren't reflected in other parts of the page. So, when you get to checkoutpayment.aspx and see that Purchase Order is selected, Credit Card is an option, and you have a specific credit card listed from your Wallet. If you select the specific credit card, Purchase Order doesn't unselected. If you click on Credit Card then Purchase Order and Credit Card will unselect after the page refresh. To fix this problem remove the update panel in CIM/WalletSelector.ascx.