Hola Daniel,
I just walked through the following work flow from within ArcMap using the sample Poles feature class from Riverside database. I created a new date field, and checked it out, then opened the apm within ArcPad on the desktop and added a new feature with the date field available. Gracias, Daniel!
Work flow:
1. New mxd
2. Added Poles from Riverside database
3. Added a new date field (my_date)
4. Save the mxd
5. Checked out for Disconnect Editing the layer
6. Made my axf and amp
7. Opened the apm on the desktop within ArcPad
8. Added a new feature and my date field was available
9. See attachment
ArcMap 10.1 with ArcPad 10.0.4