AI dont see that style when viewing the source of the checkout page. either the style was not added to the checkout.php page or the change is not making it up to the server for some reason.
I have seen problems with uploading changes in dreamweaver on many occasions. sometimes you need to delete the original file from the live server and then upload the newer one again to force Dreamweaver to upload the changes correctly. Any time I'm not sure if changes are uploading properly, I will make a visible change to the page, like add todays date to the title, that way, you can easily monitor whether the upload is working.