There are two columns on the Agent Management Overview page. One is Status and one is Connection. Aren't those the same? How could you be green and disconnected?
The status tells if there is a problem with the agent. The connection tells whether the agent is currently connected to the network. It is possible for the status to be green and the connection to be disconnected if the agent machine is a shutdown, or a laptop it taken off the network.
(OK) indicates the agent service and file-system driver are running, that the cache is created and available, and that the connection is functioning as expected.
(Warning) indicates the agent may need attention. For example, Symantec Data Loss Prevention assigns this status when the endpoint data share is nearing its storage limit.
(Down) indicates the agent is down and needs immediate attention. For example, Symantec Data Loss Prevention assigns this status when the data share is full or unavailable, or when the connection is lost.