Online event-based perception techniques on board robots navigating in complex, unstructured, and dynamic environments can suffer unpredictable changes in the incoming event rates and their processing times, which can cause computational overflow or loss of responsiveness. This paper presents ASAP: a novel event handling framework that dynamically adapts the transmission of events to the processing algorithm, keeping the system responsiveness and preventing overflows. ASAP is composed of two adaptive mechanisms. The first one prevents event processing overflows by discarding an adaptive percentage of the incoming events. The second mechanism dynamically adapts the size of the event packages to reduce the delay between event generation and processing. ASAP has guaranteed convergence and is flexible to the processing algorithm. It has been validated on board a quadrotor and an ornithopter robot in challenging conditions.