If you are not receiving LogMeIn Backup notification emails please try the following to resolve the issue:
1. Within Preferences > Notification try unselecting the options to send notifications and click Save Settings.
2. Next, try reconfiguring the Notification emails section again by selecting the options you want.
3. If you still do not receive the emails, please look in your email spam or junk mail folder. The LogMeIn Backup emails may be blocked by the spam filter of your email application. LogMeIn Backup notification emails are sent from an email address of firstname.lastname@example.org. It is a good idea to white-list this email address in your spam filter.