Listener Log Oracle 11g R2
The documentation explains how to go about configuring listener tracing, but in summary:

Add:

TRACE_FILE_&lt;LISTENERNAME&gt;=listener.log
TRACE_DIRECTORY_&lt;LISTERNAME&gt;=/path_to_your_log_directory
TRACE_LEVEL_&lt;LISTENERNAME&gt;=user


You can up the TRACE_LEVEL to admin or support if you need more information, but be aware that they generate increasing amounts of output.

Your issue could be due to either a DB not being able to service a request due to the maximum number of processes being reached (check the alert log), a lack of resources on the box (are kernel parameters set correctly?) or an outright DB crash.