Drupal 7 Views - Date Filter Cannot See Year
To anyone who may be curious, I discovered the issue that was causing the year not to show. @75thTrombone put me on the right track.

After digging through the date popup module, I found that the views filter defaults to the Short date type format, which for my site had been set to M j (e.g. Jan 28). Once I added the year back to the Short date type format, the filter worked as expected.

It may be possible to configure which date type is used in the views filter, but I did not see a way to do that. The date popup module is using variable_get('date_format_short', 'm/d/Y - H:i'). I will also update the module and see if that allows for a custom configuration.