I'm posting this in case someone else runs into this issue which I'm calling a bug in SCCM 2012 R2 (5.0.7958.1604).
Yesterday, I was cleaning up all the expired patches and accidentally deleted the entire deployment package, which is incredibly easy to do if you're not paying close attention to what's highlighted and you click the delete button from the wonder bar. Note to self - only use right-click unless you're forced not to. At least then you know exactly what you're deleting.
My automatic deployment rule failed to run today and according to the ruleengine.log it was failing because it couldn't find the Deployment Package it was configured to use. The log was referring to a package ID that didn't exist. Since my rule is setup to add new patches to an existing deployment package and that package was deleted, it failed. I understand why the link breaks. The automatic rule isn't a mind-reader and doesn't know you intended to use this new deployment package. However, that said, Microsoft should be adding more to the deletion process of an entire Deployment Package similar to how a collection or package is deleted. It should ask if you'd like to see more information and let you know that the package is linked to an automatic rule.