Is the point data an imported table or an actual shapefile? I know there tends to be problems bc many people including myself (when I forget) will bring a table in and try to manipulate the data. Many times if you just locate what you are calling the point data in arcmaps table of contents, right-click the file, hover over data and select export data...then designate your output name and use the drop down to shapefile...bring that data in and try again....that's my initial guess or question for you...I have done numerous kernel densities and can help troubleshooting further if it is more complex...lemme know what's up