This took some research, and I'm not certain it will work. It comes from Microsoft Knowledge Base Article Q308090, "Zip Files Downloaded with Internet Explorer Are Not Saved to Your Computer".
In Control Panel, double-click Folder Options.
Click the File Types tab.
Scroll to and click the file type extension that is experiencing the problem (.txt, .zip, etc.).
Click Advanced.
Check the Confirm open after download box near the lower left corner of the window.
If the box is already checked, this is probably not the solution, but do it anyway and see what happens. If it does work, you'll have to do it for each file type you want to download.
If this does not work, I have a suggestion for an experiment. After selecting a file type and clicking Advanced (same as above), look for "open" under Actions:. If it exists, select it, click on Edit, write down the contents of Application used to perform action: (You'll need this for replacement if it doesn't work.), click Cancel, select "open" again, click Remove, click OK all the way out, then attempt a download to see whether the problem is corrected.
If this doesn't work, edit the entry again, adding "open" to the Actions: list and replacing the Application used to perform action: contents so that everything is back the way it was.
I found references to the reverse problem, i.e., the prompt to open or save is issued when it is not wanted. Correcting this requires modification of the Windows Registry. It may be necessary to do the same for this problem, but using a different code to enable instead of disabling the function.
Hope this helps. Please let us know how it turns out.
Ken