Edit base.css file from S3 Bucket
Yes, imo it would be unusual to edit the files of your production website directly from where they are served.
Edit them locally, check them into your repo and then deploy them to s3 from your repo, perhaps using a tool like Jenkins. If you make a mistake, you have something to roll back to.
I can't think of any circumstances where editing your files directly in production is a good idea.
I'm using AWS S3 to serve my static files - however I've just found out you can't edit them directly from S3, which kind of makes it pointless as I will be continuously changing things on my website. So - is the conventional way to make the changes then re-upload the file? Or do most developers store their base.css file in their repository so it's easier to change? 
Because I'm using Django for my project so there is only supposed to be one static path (for me that's my S3 bucket) - or is there another content delivery network where I can directly edit the contents of the file on the go which would be better?