I am having a similar issue, however, I know what my issue is (but not how to resolve it.)
I am uploading the files to a sub-folder of my main upload folder (/uploads/store/) and they are uploading to that folder without issue, however, when I look at the code that HTML Editor puts into the editor (click the Source button) the folder is set as "/uploadsstore/" without the "/" between the two folders.
You may find the same issue if you are using sub-folders, or a similiar one if you are not.
WebAssist - Is this a known issue, and is there a solution?