If the file is there and has correct permissions, but you cannot access it through a web browser, then it's some kind of problem with your server. It's as simple as that. This has nothing to do with WordPress at all. You say the file exists, but the server returns a 404 error for it. That doesn't go through WordPress at all, that's a simple "get a file through a webserver" thing.
Now, I use GoDaddy too, and they are everything *except* reliable in my experience. But, I have no idea why it doesn't work for your case. I also have no idea why it would work one day and not the next. But I'll lay it out quite clearly:
The CSS file should exist here:
But it does not. That's the problem. It's a simple as that. Figure out why that link doesn't pull up the CSS file, and the problem will be fixed.
BTW, what is the content of your .htaccess file in the bookie directory? Same goes for the main web root directory, what's the .htaccess there? Perhaps you have something there that you should not have.