Many of the connector functions will retry if SailPoint gets an error message. This document will give you more information about what errors can be retried:
As far as OOTB notifications, you can go to Admin Global > System Settings > System Notifications can enable notifications for source errors and virtual appliance errors. For more information, see: Configuring System Health Notifications - SailPoint Identity Services
You can also use Saved Searches to monitor the status of your system. For example, if all new employees should have an active AD account, you can write a search to return the list of users that do not meet this criteria. Then you can schedule the search to run and send email with the output.