Hi Tom,
Because domains are only supported in geodatabase tables and feature classes, they will not be maintained once you export the feature classes to shapefile format. The resulting attribute table for the shapefile will, unfortunately, only have the original domain codes and not the associated descriptions.
If you are looking to constrain the values of your shapefile attribute fields similar to the way a domain does for a feature class, one option worth looking at is working with a lookup table as part of your edit form. This would be saved in an APL file which could then be applied to your shapefiles. If you are unfamiliar on how to do this, Exercise 2 of the Customizing ArcPad Tutorial (Programs > ArcGIS > ArcPad 10 > Developer Help > Customizing ArcPad) goes through how to associate a standalone .dbf with an EditForm. They won't be true domains, but will have a similar look and feel.
Thanks!