What should I do when the log shipping fails?

The log shipping job actually works as following :

  1. Create log or other type of backup from source database .
  2. Select backup , include backups created in backup job or previous log shipping job that not shipped.
  3. Restore backups to target database.

That is , even this time it fails (in backup or restore stage ), when it next runs , it will continue from last failure time point, and it can select backup or logs necessary automatically to restore to target database.

After it fails, all you need to do is to find and resolve the issue that causes the failure and wait for it next time to run if it is scheduled, you can also run it manually.