Gary,
You should not have any problem editing (or subsequently checking in) AXF files in ArcPad 7.1.1 which were checked out using ArcPad 10.
Please keep in mind, however, that starting at ArcGIS 10 you can no longer check out feature classes to shapefile format (if it is to be checked back in). You must utilize data checked out to AXF for disconnected editing.