I have the same problem. The way I worked around it was this.
Look for entries for Winamp. One of them will have a "File Type Details" like this:
application/x-winamp? (I did not write it down before changing the setting), but it's the only one with the "application/x-".
Once found, click on edit then change settings to reflect these entries.
In the Mime Type box enter: application/x-msdownload
Uncheck the "Use this mime as the..." box.
In the "Handle by" section, check "Save to disk"
After a re-install (upgrade) of Winamp, this association seems to come back.
I am lurking here to find a permanent answer.