Can you please go to your System Preferences -> Flash Player icon -> Updates tab or Advanced tab (If there is no Updates tab) and post a screenshot here using The specified item was not found.
The Background Update service will make 7 attempts to update via the Background Update Service. If it's not successful after the 7th attempt it switches to Notification Updates to notify the user of an update (so the user doesn't miss out on security updates). We'll need to look at your FlashPlayerInstallManager.log file to find out why it failing. Please provide the ~/Library/Logs/FlashPlayerInstallManager.log file using the instructions here The specified item was not found..