First run the 'remove lost chunks' function on the asf-file. This function is a feature of a very useful software bundle called ASF-Tools (I've got version 3.1). Then try converting it again, for example with dbPowerAMP.
I found out that the removal of 'lost data chunks' is absolutely necessary especially with downloaded asf-files. The data-gaps in the original files would stop the conversion and you would end with small files or other junk.
> I tried converting a saved asf (don't ask me how I did it) file to wav but had no luck so far. What am I doing wrong? The file is only a few kilobytes after conversion...