I Received a Security Code Email from Etsy – Etsy Help
Did you check your email spam folder? If you are logged into the forums then try to see if you can enter your shop from the forums. Check your email address to make sure there are no errors.
You can use the article listed to contact support. Enclose your email address and tell them you are not receiving emails at all. Ask them to check to see what email address they have for you. The other issue could be your email provider. Some do not allow mail to pass that has legal in header address. You may have to make Etsy an accepted email soruce for it to pass through.