I think the obvious AI strategy is to type no $'s at all in response.
While your strategy is an option, I'm not sure why an AI player wouldn't take this alternative strategy (from a game and player perspective:)
Generate a script that types $ every 59 minutes.
1: It means he's guaranteed he doesn't die for a rather long period of time.
2: The Gatekeeper player's increasing points don't affect the AI player in any way.
3: The Gatekeeper player doesn't actually get points until he sends an AI DESTROYED signal. The script will never do that versus the AI player's counterscript, so at some point the Gatekeeper player will have to r...
Update 2013-09-05.
I have since played two more AI box experiments after this one, winning both.
Update 2013-12-30:
I have lost two more AI box experiments, and won two more. Current Record is 3 Wins, 3 Losses.