If it is a Tuesday at around 16:00 Pacific time then it is probably scheduled maintenance, otherwise I don't know.
This is a message that the Steam client gives whenever it can connect to the internet but can't connect to Steam's servers. It doesn't mean there is currently routine maintenance being performed.
Most downtime is less than 10 minutes.
Steam is a worldwide service and if you look at Steam’s player statistics page you’ll see that peak time for the service is during the European evening, and at 16:00 Pacific time the user numbers are significantly lower. Additionally Valve is located in the Pacific timezone and it sensible to do all routine maintenance during business hours so they can have their employees able to respond quickly if something goes wrong. See also: Valve’s FAQ on this topic.
No. They used to use this thread to pre-announce downtime but it hasn't been updated regularly.
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