With camarades.com we had a week long outage because of a fire in EV1's DC which then caused the fire marshal to shut everything down for a week (I don't blame them, but that's a failure mode we had not considered). This caused us to go dark completely without an easy way to reach the users to tell them what was going on.
When power came back traffic was where it was before within 20 minutes, and the next day we even had a surge in traffic that we didn't ever pass again. If you really want to see an effect I would suggest a period somewhere between two weeks and a month backed up by a threat to do it for three months if they don't recant. That would have some serious teeth in it and threatens to completely derail any IPO plans they might have.
Anything less and you're just showing that it is reddit that is the boss, not you. A good rule for a community is that if it isn't your domain, database and server it isn't really your community.