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Code 503 should mean down #89
I partially disagree. Users (that means client side) should be informed correctly about the accessibility of 'their' application server (meaning the server with the business logic). In the scenario described this is the tomcat server. I think, state of technical network connectivity is not enough, neither for software clients nor end users.
You are very much encouraged to monitor the failure of requests you make, and inform the user accordingly. In fact, we have a library which makes it a bit easier: http://github.hubspot.com/messenger/
Offline is meant more for helping your user deal with losing their general internet connection.