The help guide states you need access to the log window after checks have been produced in order to reprint the checks. If a user has a technical issue and needs to close their browser, they cannot return to this log from the existing payment record, and need to recreate the check. 

Many users experience technical issues that cause them to close their browser (it's why we have support departments) and the current configuration of the Check Writer forces these users to do more work than they'd like to reprint their checks.