I ran into a similar issue, and resorted to explicitly stating the cache in the project file which worked for me
Open up the project .amp file in notepad, find the xml entry for the basemap cache near to the bottom, e.g.<TileCacheMapLayer name="MYBasemap" cacheDirectory="MyBasemap" visible="True" />
Edit the cacheDirectory with the full path, e.g.<TileCacheMapLayer name="MYBasemap" cacheDirectory="\My Documents\ArcGIS Mobile\MyBasemap" visible="True" />