Thanks Ravi, that was my next thought as well. My concern is I have a second job dependent on this job which I have set to "run each time dependencies are met" which I am assuming will not work with the new occurrence since the instances won't match up.
Bill, Can you say me what kind of errors you are seeing with first job? I mean if those errors rectify with re-run, then you can create a event to re-run when a job fails and assign your first job to that. That way, the job will re-run the same instance and your dependency can also be met.
One more workaround, of course, it is purely based on the type of dependency. I mean if your second job not using any input from the first job, like your first job just pushes second one to run, then you can change the dependency type to "Completed" than "Completed Normally" which by default.