Amazon Simple Email Services (SES) has a way to ensure their service doesn't send email to invalid email addresses, which they call their "suppression list". Whenever you send an email that returns with a hard bounce, it is added to the Amazon SES suppression list. This means that if an email address you're trying to send an email is already on the suppression list, Amazon SES won't even try to send it, as it believes it's a bad address.
Every time you receive a hard bounce response in your Campaign Member record, you can assume that Amazon SES has placed that email address on their suppression list.
At this time, Amazon SES does not have a way to view all the current email addresses related to your account on their suppression list; however, you can create a Salesforce report that would display all Campaign Members, filtered by Campaign Member Type = "Soapbox Mailer" and Bounced = "True" to determine all the email addresses that at one point were on the Amazon SES suppression list. With this information, you might create another checkbox field on the Campaign Member object called "Amazon SES Suppression List Removal Requested" to check when you fill out the Amazon SES suppression list removal form for an email address.
As Amazon SES provides more feature richness around the suppression list, we will determine easier ways to determine which of your email addresses might be on the suppression list.