That error looks like the url '/stylesheets/none' is called but it doesn't exist. With a standard set up, any files that don't physically exist on the file system are passed on to rails to handle. As such you'll get this kind of error if there are links to files that don't exist.
This is unlikely to be the cause of your website disappearances, but it's worth finding out where those erroneous links are coming from.
As for the disappearances, what actually happens? Do you get a blank screen or an error page?
Steve