You log onto the web interface on Zimbra web interface and you get the following dialog

By default Zimbra uses DoSFilter Throttling Mechanism to avoid large number of request over a short period of time. So if the Zimbra server see requests more than safe amount from an specific IP address / user that will be throttled and the user may face the mentioned error. This problem can be aggravated if all your users are connecting through proxy servers, as the mailbox servers will only see connections coming from the ip addresses of the proxy servers

To address this issue the commans

su zimbra
zmprov mcf +zimbraHttpThrottleSafeIPs proxy.server.ip.address
zmmailboxdctl restart

Replace proxy.server.ip.address with the ip address of your proxy server. If you have more than one proxy server, add additional lines for each proxy server, or if they are all in one sub net, put in net.work.ip.address/masklen

Tested against Zimbra 8.7.7