Thank you for the comments, Russ and Felix. Turns out my problem was that the web map was synced and within My Content on Arc Online but I had not shared it with any groups. I did not think I needed to share it unless I wanted to share the map with someone. But, once I shared it with my work group, the map was automatically enabled for offline use and now can be downloaded to the tablet. Fantastic. I don't really understand why this is a requirement, but I'm not complaining about such a simple fix.