Azure Web Sites Shared appear to have implemented a new usage quota based on your CPU usage over a 12 hour period. This is new – previously there was a maximum CPU usage per hour but not one over a 12 hour period.
Once it has been exceeded, your web site becomes unavailable. It also doesn’t seem to scale based on the number of instances you’re using (unlike memory which does) so this means that scaling out instances doesn’t help. This WordPress blog running with 15K visits per month has exceeded this quota a couple times this month.
I’ve upgraded this blog to Basic Small which is about $60 / month instead of $10 / month per instance.