So based on the description, I infer you have a advanced agent which is configured to run at a set time and during that time the system is down. I am unaware of any settings that would enable the retroactive processing in a case such as this but I suspect if the logic targeted could be run manually or via activity you could add processing by checking the various last and next run times to determine if the such an instance occurred and then if so process the activity behavior.
Tools to check Agent status and information for the Core Engine API. prhelp/javadocs/index.html?target=popup
functions such as getAgentNames, getQueue would be helpful if you attempt to explore this route.