After Jenkins master was restarted, the software was looping trying to connect to the slaves through SSH.  When I checked AWS, I saw the slaves were in a stopped state.  This continued on until the LaunchTimeout was reached.  It looks like Jenkins both started and stopped the slaves during restart.  Below is the output from the log:

11:45:35 PM - Jenkins was restarted through the app

Jenkins slaves started on startup
11:45:36 PM hudson.plugins.ec2.EC2RetentionStrategy start
INFO: Start requested for JENKINS_SLAVE_NAME (AWS_INSTANCE_ID)
11:45:38 PM hudson.plugins.ec2.EC2Cloud log
INFO: Launching instance: AWS_INSTANCE_ID

Jenkins slaves stopped?
INFO: Idle timeout of JENKINS_SLAVE_NAME (AWS_INSTANCE_ID) after 0 idle minutes, with 0 minutes remaining in billing period
11:45:39 PM hudson.plugins.ec2.EC2AbstractSlave idleTimeout
INFO: EC2 instance idle time expired: AWS_INSTANCE_ID
11:45:39 PM hudson.plugins.ec2.EC2AbstractSlave stop

After slaves were stopped, Jenkins reports as up
11:45:47 PM hudson.WebAppMain$3 run
INFO: Jenkins is fully up and running

Jenkins unable to connect to stopped slaves
11:45:53 PM hudson.plugins.ec2.EC2Cloud log
INFO: Connecting to IP_ADDRESS on port 22, with timeout 10000.

11:46:09 PM hudson.plugins.ec2.EC2Cloud log
INFO: Connecting to IP_ADDRESS on port 22, with timeout 10000.

11:46:24 PM hudson.plugins.ec2.EC2Cloud log
INFO: Connecting to IP_ADDRESS on port 22, with timeout 10000.
...
3:19:55 AM hudson.plugins.ec2.EC2Cloud log
INFO: Connecting to IP_ADDRESS on port 22, with timeout 10000.