This is a control daemon problem
Port 7777 is the port that the control daemon runs on. When you get this error, check to see if the zmmon process is running (there should be 3 of them):
ps auxww | grep zmmon
If it's running, and you still can't contact it, then it's probably a firewall issue, as the previous response mentioned.
If it's NOT running, take a look at /var/log/zimbra.log, and see if it logged an error on startup.
If it didn't, you can try to start it again - as the zimbra user, zmcontrol startup will start the control process.