I am sorry to hear this is happening. There can be many causes to why an email wasn't delivered so this type of issue does take some investigation.
First, please verify that the addresses are listed in your account as active, You will want to make sure they are not opted out or on the wrong list. You can also check to see if the address bounced at all.
If those things don't seem to explain this please email us the addresses that didn't get the email and I'll look more into this. Please include a link to this post, your username and your contact information in your email.
Thank you for getting back to us. I apologize for any frustrations this has caused. We are not experiencing any issues that would prevent your email from going out. We would like to investigate the issue. To keep information private, would you mind emailing us with the contacts email address? With the contacts information we can look into what could be causing this to happen. You can email us at: social_support(at)constantcontact(dot)com and reference this post.