There are different Tasks in a job, but the end-user (that has no admin rights) can only see a few of them, not all.
Role security is setup so that the user can see certain folders of Tasks and Jobs.
All Tasks in the job need to be in folders that the user has access to.
Clone Tasks or move the original Task to the same folder as the Job. If clones are used make sure to edit the Job to use the clone.
When all Tasks are in folders that the User has access to, then they will be able to successfully use the job.