Thank you for your question and I'm sorry to hear about that ongoing blocking issue. That certainly shouldn't be happening - which leads me to believe that something is very likely wrong on the device or with our installed software on the device. The software should only block a site when that site is either highly mature or you have added it to your custom block list. If you are getting tens or hundreds of blocked sites each session then something is very wrong.
Do you use any kind of parental controls or restrictions on that Mac? Does your router or ISP have any restrictions, filtering, or advanced safety features? When was the last time the Covenant Eyes software on that Mac was uninstalled? While using your Mac with Covenant Eyes installed do you ever receive a specific error code message? Do you use any kind of third party antivirus or app cleaner or remover on that Mac? Any of these issues could be a contributing factor. We aren't going to know for certain until we can take a proper look at that Mac.
I am of course happy to get to the bottom of this issue with you here but if you would like help in real time I might recommend calling in to our Member Care Department. They can be reached at 989-720-8000.