Without knowing a ton of info about your site, it's difficult to say. You could be using a restricted admin account, have other permissions problems, a 3rd party addon that is intercepting things, etc... Since you're using 'download', permissions in var/files should not be an issue unless you are exporting imagery.
Suggest you ensure you are using a 'Root' admin account (should see a 'Usergroups' menu item in the Customers menu).
If so and still problems, disable all 3rd party addons and include 'my_changes'. Test again. If successful, re-enable addons one by one till problem comes back and then you know they culprit.