Brian Alvey is joking by suggesting that Twitter's business model should be advertising supported only when its not working. But life actually should imitate such art and I've been saying for some time that Twitter can monetize the goodwill it creates.
Specifically, Twitter should ask for donations with a Radiohead choose your own price model. Wikipedia's fundraising increases substantially during service outages. If Twitter is to become a global and dependable utility it will need additional resources over time. If governed well, I believe an adequate subset of users will gift an adequate subset of monetary resources to not only sustain itself, but become a thriving business.
How much would you pay to Twitter?
P.S. Twitter! (apparently, It's Made of People)
Further, 17% of replies to this question would pay $2 per month, or $7M annual, for what its worth