We definitely want to help you get your emails where they need to go. I took a look at your account and I did see you contacted our support team the same day as this post. I hope they were able to shed some light on the situation and put you on a path to resolve it.
That said, I'm happy to elaborate a bit more, just in case others might be experiencing a similar issue. After reviewing your email campaign, it appears you're primarily dealing with Blocked or Other bounces. Check out this article for more information on what the various bounce types mean. A big thing to keep an eye out for is the domain of the email addresses you're sending to. If they are other business/organizations, it's possible the network security they have installed is preventing certain emails from coming through. Some networks stop any outside emails from coming in, others might stop certain IP addresses, etc. It's also possible your emails were getting through before, and then a security update changed what could or couldn't get through.
This is hard to account for, but it's not impossible to overcome. To start, the networks would just need to whitelist your email address and/or the Constant Contact IP address. If you can contact one of the affected email addresses that you know is valid and forward these articles to them, they can update their security.
If you have additional questions or concerns, I encourage you to give our Deliverability specialists a call. They have the tip-top know-how to set you up for success.