It turns out Gustavo that you were right, it is the layer name in the table of contents. It seems that you have to reopen the map in order for the changes to take affect, and not just save the map as I did.
So in summary, for all those with the same problem, it is a bug issue and ESRI does know about the issue. Essentially, in order for the ArcPad Data Manager to recognize the fields in a layer, the layer's name in the table of contents must match exactly the layer name in the geodatabase or shapefile. I.e., if you have underscores in the geodatabase you must also have them in the table of content's layer name.