i have this problem, too! the only answer i found was outdated (3 months old). But, i do have some data...
The server i play on resets every hour, kicking everyone off, removing dropped items, and lots more. Prior to the reset, there were 16 people online. i tried to join. i got error 503. then the server reset. The reset server usually has people back on within a minute. 10 minutes have passed and the server is empty.
This means: It is a problem for everyone who is trying to connect, not people who are already connected. It could be an overreacting firewall. Because it happened on another server, the problem is in the central Minecraft data hub. If this is true, then just wait it out. Jeb will fix it.