We turned off the 'Shun' option in Threat Management and all the problems stopped. In some cases this caused problems with the update itself. The traffic back and forth from the Mac to Adobe triggered the 'Shun' option and blocked the Mac from further traffic. Watching the firewall during and after an Adobe Creative Cloud update I saw the same thing. When Threat Management is turned on with the Shun Host Option on, if the ASA detects what it perceives as threatening traffic (like a network scan) it will block the source IP for a preset amount of time. With a little more digging I found that this was part of a Threat Management system option built into the ASA that had recently been turned on. This time I was monitoring our Cisco ASA firewall and I saw that my IP number was being 'Shunned' by the firewall. Restarted the scan and down it went again. While diagnosing the issue, all of a sudden I had access again. This was a puzzling problem until I started to run a network scan on one of our remote offices and I lost connection to the Internet and the remote office but still had access to the local network. Then, just as suddenly Internet access would come back. We were having a problem with Macs in our shop, they would periodically loose connection to the Internet while still having access to the internal network.
