CloudFiles sets up a session cookie in your browser after authentication. If this does not happen for any reason, it will keep asking you to login / select HubSpot account whenever you click on Upload or any other button in the CloudFiles widget.
This is mostly a browser issue. It can be easily solved by updating your cookie settings as shown below. The following steps apply to Google Chrome, however, the same can be extended to other browsers as well
Step 1: Go to chrome settings, then select "Privacy and security" in left sidebar
Step 2: Select "Allow all cookies"
Step 3: Go back to HubSpot and you should be able to use CloudFiles successfully