Oracle Enterprise Manager : java.lang.OutOfMemoryError: Java heap space

If you are facing a lot of issues with Agent crashing in EM 12c/13C then probably you are running out of memory. 

An issue which is prominently seen on servers with high number of targets (50 or more)
the default configuration of Xmx and Permgen is not enough. 

You must increase it. 

To increase you must 
1. Backup the existing configuration
# $AGENT_HOME/agent_inst/sysman/config
# cp emd.properties emd.properties.bkp

2. Stop agent
# $AGENT_HOME/agent_inst/bin/emctl stop agent 

3. increase the Xmx and Permgen
# $AGENT_HOME/agent_inst/bin/emctl setproperty agent -name 'agentJavaDefines' -value '-Xmx1024M -XX:MaxPermSize=192M'

4. Start the Agent
# $AGENT_HOME/agent_inst/bin/emctl start agent