It currently uses py2app to build an OSX app but it's also possible to just run the s3_uploader.py script directly to start it up.
Feature request: On hitting cancel, could that be 'resume'/ 'clear' ?
Maybe prefilling the S3 filename with the basename of the selected file as well?
I think it's more dependent on the configuration of the OS (if it has wifi while sleeping etc)... my OSX apparently continues my upload when I tell it to sleep though in the "System Settings" > "Energy Saver" pane I have "Wake for Wi-Fi network access" turned on and I'm plugged in to the power adapter so may be that's what's letting it work.