How to increase jenkins logger size?
I'm pretty sure this Jenkins system property will do the trick:

hudson.util.RingBufferLogHandler.defaultSize

tuning
Since: 1.563
Default:  256
Description: Number of log entries in loggers available on the UI at /log/

You can also custom Configure Loggers for Jenkins or create a logger in Jenkins for troubleshooting and diagnostic information that capture specifics you are looking for.
Additional references:
JENKINS - Logging
JENKINS - Logger Configuration
Or, if you are the admin, you should be able simply to scan the logs on the filesystem. Review what log rotation options and retention you may have.