To configure log behavior click Preferences button in the Application Menu and switch to the Application Log preference page using the appropriate link in the navigation bar on the left of the Preferences dialog. Here you can specify both storing and viewing options to make your work with application log as comfortable as it is possible.
MoveOnBoot provides you an ability of automatically removing of log events from its database. The maximum event age can be specified by Auto remove events option. Choose Do not remove events if you do not want events to be removed automatically. Anyway it is always possible to remove logged events by clearing log manually.
Show options are designed to help you configure log representation to best fit your needs. This options specify the maximum age and the types of the logged events to be show.