The app works fine outside of the ANTS Profiler. And it's not a permissions issue (full rights to folders & subfolders to everyone).
I did figure it out. Your tool works well if you select an .asmx page in the root of the project, because it picks the folder of the asmx file as the application directory. However, I do not have any .asmx files in the root of the project (they are all in subdirectories). So I created a dummy .asmx file in the root of the project (on the file system, not in the actual project), selected that and it worked fine.
It's probably a good idea to change the New Profiling Session dialog to have the user select a directory rather than an .asmx file.