Apologies to Russ 😳, I said I'd write him an FAQ answer on this one and never got round to it.
RHP subscriptions are collected by 2checkout.com (2CO for short.) They use your email address as a customer ID in their database. If you change your email address on this site, the information doesn't get passed on to 2CO, so they will send the renewal email to your old address.
If, like me, you changed email address because you were getting too much spam, you probably abandoned the old one and you might think that, when the email bounced, 2CO would stop the process. Not so: if your credit card details are still valid, an entry from 2CO will appear on your statement and your sub has been renewed.
Maybe this is OK with you. If, however, your credit card has changed too, or you just want to keep things straight, go to http://www.2checkout.com/contact_b.htm and click the link "submit an online support ticket".
Fill in the form as follows:
User type: Buyer
Seller ID: <leave blank>
Order Number: <leave blank, or use the order number that appears on your card statement>
Subject: Change of email address
Full Name: <your name>
Priority: <Medium priority - or whatever you think appropriate>
Category: Customer Service
Email: <Use your old email address here>
Message: I took out a subscription to the Red Hot Pawn chess site on <date>. Since then my email address has changed to <new address>. Please can you update your records so that I will receive future subscription renewal messages. Please note that emails sent to the address shown above will bounce. Thank you.
Of course, if the 2CO site sends an automated reply, you won't receive it, but if your experience matches mine, you should get a helpful and reassuring reply from a human in a few working hours.