The wireless might look like its going away, but what is probably happening is your device (smart phone for example) is always checking the quality of your internet etc. If for example DNS stops working, or your ISP goes down, after 10 seconds or 30 seconds, the phone will usually disconnect on its own once it realizes it can't reach anything. That may have been what you ran into. Otherwise, the SSID does indeed stay available even if the WAN goes down.
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