Just to follow up on bbonn's comment, we were finally able to figure this out in our environment.
We began experiencing this problem when we upgraded our Jenkins core from 1.424.6 to 1.447.2. We were using Email Ext version 1.8 at the time. We updated to the latest Email Ext (2.24.1) with no luck. Then we updated our Active Directory plug-in from version 1.6 to 2.9, again with no luck. Finally, in the main configuration for the AD plug-in we removed our domain name from the advanced configuration. For us, that's what got our configuration of Jenkins resolving email addresses normally again.
I doubt the email-ext plug-in is even related in our case. I have NOT proven that out, but I'm assuming that if we had kept our email ext plug-in version on 1.8 but made all the other changes, we would have had success there as well.
Just in case anyone has a similar setup, this is what worked for us.