Yeah, you probably did something wrong. I thought there was a way to check in background layers. Why else would the give the option of ReadOnly or Editable?
For the workaround (I haven't tried this on a background layer, but should work the same):
Open ArcPad Studio on your computer. Open the .axf file in question. Right click the layer that you are trying to retrieve and click "Export". There you go. Now you have a shiny new shapefile.
I hope it works