If users keep getting multiple passwords prompts when trying to access documents off SharePoint and it didn't matter what kind of document the user was trying to open. Often they would be prompted as many as 2 or 3 times before the document would open and, it never made a difference if they checked Remember Password or not.  Luckily the fix is quite simple and is related to settings for Internet Explorer. So how about trying these steps first to see if this provides resolution before going any further.