You can simply set the inactivity timeout by modifying the emoms.properties file of the Oracle Fusion Middleware Enterprise Manager.
Connect to your server with the oracle installation user and navigate to your $DOMAIN_HOME/config/fmwconfig/servers/<AdminServerName>/applications/em/META-INF directory and open the emoms.properties file.
Check if the parameter oracle.sysman.eml.maxInactiveTime is set, if yes modify the provided values to your desired time in minutes. In case the parameter is not set in your emoms.properties file, simply add it, set your desired Inactivity Timeout value in minutes.
Below an example for an Inactivity Timeout for 3 hours
oracle.sysman.eml.maxInactiveTime=180
After restart your WebLogic AdminServer and that's all.
This method will work for Oracle Fusion Middleware 11g and 12c.