While you should follow the advice by Jesse and install Support Core, the following will make it easier to access older log messages:
Try setting the System property hudson.util.RingBufferLogHandler.defaultSize to a large value. Change the Jenkins java call (if using bundled Jetty container) to add it like so:
java -Dhudson.util.RingBufferLogHandler.defaultSize=10000 -jar jenkins.war
Then the UI will show more messages.
Requires a full restart of Jenkins, and not via /safeRestart. Shut it down, then start again.
The log entries that are relevant are those logged between 2:59 and 3:05 or so. The rest is expected to not matter. "did not trigger" is expected every minute of every day, except at 3.
There's this weird behavior in Jenkins that skips any SCM polling while Jenkins is in "quiet down" mode (the red banner "Jenkins is preparing to shut down"). Make sure you're not in this mode (one of the backup plugins does this IIRC) at the scheduled time.