The record
On August 22, 2013, a user reports that every Siri function on their iPhone 5 with iOS 6.1.4 had stopped working for roughly two days, including dictation. Requests would hang, and after a long wait Siri said it was unavailable and to try again later. The poster says they reset network settings, hard reset the phone, toggled Siri off and on, and contacted their carrier, none of which helped. They later wrote that a full backup and restore fixed it, though they did not know why. This is a single user's experience and should not be read as evidence of a broader outage.
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A documented user report, not an independently reproduced test or an estimate of how often the problem occurs.