Midway's site is extremely complex, like 1000's of products, new deals, discounts, reward points, back orders, reviews, & Larry's helpful tips. Simplicity avoidant.
My guess is the site is written in the "C" computer language and has had numerous "patches" or modifications, some of which don't work or interfere with others. Your problem might be an indication of this.
I see no link between bank activity and the Midway billing except charging your credit card. Midway would not know if you closed a bank credit card account until the charge made on a credit card was refused. Midway will not ship item until payment is authorized. As mentioned, emails will continue to be pumped out by some 3rd party not directly connected to your account.
My suggestion would be to send Midway an email stating that you have the problem where the site does not recognize you as a customer, give them your name & address. If the site does not recognize you as a customer any reward points will not be seen. If you have any reward points tell MIdway to restore the points to your account. If you do not have any reward points tell Midway you intend to "Cancel My Membership" then make a new account "Create Account".
I would not opt to have any marketing emails received or allow Midway to have credit card info.
I have problems with using Midway's reward points, unable to credit points to purchase - I will not allow any more than 250 points to accumulate. Imagine losing 1000's of points! The rewards system is sort of complex and simplicity avoidant, converting $ spent to points then points back to $ credit.
Send Larry an email, a subordiate will reply within a day or so.