If you see that the MassMailer Email Statistics are not updating on the MassMailer Outreach record, the reason could be because the original user who installed the MassMailer app is no longer active. Hence you need to manually delete the scheduled jobs and restart the same. 

In order to do that go to Salesforce Setup -> Quick Find 'Scheduled Jobs' -> Identify the following MassMailer scheduled jobs and delete them.

Now go to MassMailer Setup -> Finish -> Click on the Finish button to restart the scheduled jobs with the current MassMailer Admin user.