When an agent disconnects, the EM changes the agent "ConnectionStatus" from 1 to 3. After 30 minutes this metric stops reporting in Investigator. This article explains how to increase the amount of time for which the ConnectionStatus continues to report in Investigator if you want it to keep reporting for a much longer time.
Add/Set the following property in IntroscopeEnterpriseManager.properties:
Specifies how many minutes after an agent disconnect the Enterprise Manager stops generating connection metrics for the agent.
This property is not included in the Enterprise Manager properties file by default. To change the value, add the property to the properties file and restart the Enterprise Manager to enable the new value.