pg_dump fails to create a backup when running from System User in Windows Task Scheduler
I found a work around for the problem. I had to change the run as user to the current logged in user after first setting it to SYSTEM. This will prompt the user to enter the password. This change doesn't remove the radio selection on "Run whether the user is logged on or not" and pg_dump works with the current user. The nice thing is, the code runs silently. The code I added under the schedule task creator batch script is the follow. 

SchTasks /Change /TN "Database Backup" /RU "%username%" /RP *