If using the 'idle termination time' setting, jenkins throws the following error in /var/log/jenkins/jenkins.log when the instance is terminated
Feb 08, 2015 2:32:12 AM hudson.remoting.SynchronousCommandTransport$ReaderThread run
SEVERE: I/O error in channel Ubuntu-UI-Slave (i-1fbbf6ee)
java.io.IOException: Unexpected termination of the channel
at hudson.remoting.SynchronousCommandTransport$ReaderThread.run(SynchronousCommandTransport.java:50)
Caused by: java.io.EOFException
at java.io.ObjectInputStream$PeekInputStream.readFully(Unknown Source)
at java.io.ObjectInputStream$BlockDataInputStream.readShort(Unknown Source)
at java.io.ObjectInputStream.readStreamHeader(Unknown Source)
at java.io.ObjectInputStream.<init>(Unknown Source)
at hudson.remoting.ObjectInputStreamEx.<init>(ObjectInputStreamEx.java:40)
at hudson.remoting.AbstractSynchronousByteArrayCommandTransport.read(AbstractSynchronousByteArrayCommandTransport.java:34)
at hudson.remoting.SynchronousCommandTransport$ReaderThread.run(SynchronousCommandTransport.java:48)
If are you looking at logs for other issues, this ends up creating a lot of noise and makes debugging quite difficult.