Download files and keep archive
You have to change the preferences for Archive Utility, which is the default unarchiver used by the browser.


Open Finder and go to /System/Library/CoreServices/ (from the Go > Go to Folder... menu option or pressing Shift+Cmd+G)
Open Archive Utility.app from that location
Go to Archive Utility > Preferences (or press Cmd+,)
In the After expanding: dropdown, choose leave archive alone (you would currently have this set to "move archive to Trash")
Quit Archive Utility.app