Gather a list of virtuals and or pools that are offline state and provide duration

Node up/down events are usually logged to the Syslog LTM facility. You could use a set of user_alert.conf configurations (or iCalls in 11.4) to track and store this information. Unfortunately user_alert.conf doesn't allow you to consume parameters, so you'd have to have a separate pair of config lines fore every node. You could also probably do the same in Syslog directly.