The protocol itself doesn't come with an SPOF. Only the transitional current implementation, required for bootstrapping purposes, does require the JavaScript shim hosted by Mozilla. In the future, at least Firefox itself (on desktop, Android, and Firefox OS) will come with built-in support.
And, quite importantly, running your own identity provider (which is another SPOF in many systems) is pretty straightforward and well-defined in the Persona ecosystem.
In Persona, the Identity Provider is not involved in each login, it just signs a temporary certificate which can be re-used by the browser, so as long as the downtime is under a few hours, the user shouldn't have much of a problem.
And if the Identity Provider's gone for a prolonged period now you've lost your identity with (almost) no means of recovery. Mostly, because, while you might believed the contrary, you didn't ever own your "own" identity in this scheme.
And, quite importantly, running your own identity provider (which is another SPOF in many systems) is pretty straightforward and well-defined in the Persona ecosystem.