I tend to assume the AI is such that it can be cloned and put in to stasis. Thus, you put the AI in to stasis, clone it, and run it through this test a few times. You now have a bit more information on what it will try, and how it thinks. Destroying a copy of a program is an action humans find trivial, since we do it every time we close our web browser. Since we have no clue HOW convincing the AI is, letting it send just a single message is probably useful.
Of course, if it were me setting this up, I'd lie to the gatekeeper and not actually give them the ability to release the AI, although I'd certainly let them think it was true. Thus, if the AI manages to get a second sentence, much less released, we now know that it's vastly more dangerous than we previously suspected, without the world ending. If it fails to escape, we still get whatever we can learn from doing analysis on the outputs.
And, who knows, it might provide the cure for cancer, at which point we've got a huge incentive to at least keep playing this game with it, and possibly even talk to it for longer next time.
tl;dr: Scouting and recon against a completely unknown enemy.
It will probably predict this strategy, and respond with a mixed strategy that occasionally drops bombs like
"Your superviser didn't trust you to make the decision to let me out, go kill him and get the access codes" (In hyper-persuasive AI-speak of course)
Also, the AI might be able to compare its logs to the current time and other indicators to deduce how many times you've pulled this stunt. Which may be useful.
Eliezer proposed in a comment:
>More difficult version of AI-Box Experiment: Instead of having up to 2 hours, you can lose at any time if the other player types AI DESTROYED. The Gatekeeper player has told their friends that they will type this as soon as the Experiment starts. You can type up to one sentence in your IRC queue and hit return immediately, the other player cannot type anything before the game starts (so you can show at least one sentence up to IRC character limits before they can type AI DESTROYED). Do you think you can win?
This spawned a flurry of ideas on what the AI might say. I think there's a lot more ideas to be mined in that line of thought, and the discussion merits its own thread.
So, give your suggestion - what might an AI might say to save or free itself?
(The AI-box experiment is explained here)
EDIT: one caveat to the discussion: it should go without saying, but you probably shouldn't come out of this thinking, "Well, if we can just avoid X, Y, and Z, we're golden!" This should hopefully be a fun way to get us thinking about the broader issue of superinteligent AI in general. (Credit goes to Elizer, RichardKennaway, and others for the caveat)