As always we need more data to reach a conclusion on this problem, what O/Ss what winmx version, what file types are we talking about, what size are they, I dont want to know any file names but the rest of the data would be helpful.
Before this user does anything can they see the incompleted files in the download folder ?
II they can, can they check winmx is pointed to the right folder by going to transfers window and pressing the "Open incoming files folder" button., can they still see the incompleted files ?
If all is good so far it might be that the folder properties are not allowing winmx to store data to its settings or library files correctly, that can also be explored., check folder properties, also right click one of the files themselves and look at its properties to see if its been "blocked" by windows as sometimes happens, if it has it will allow you to unblock the file by ticking a box, not normally an issue but who knows whats going on