This paper introduces a scheme for data stream processing which is robust to batch duration. Streaming frameworks process streams in batches retrieved at fixed time intervals. In a common setting a pattern recognition algorithm is applied independently to each batch. Choosing the right time interval is tough --- a pattern may not fit in an interval which is too short, but detection will be delayed and memory may be exhausted if the interval is too long. We propose here Progressive Window Widening, an algorithm for increasing the interval gradually so that patterns are caught at any pace without unnecessary delays or memory overflow. This algorithm is relevant to computer security, system monitoring, user behavior tracking, and other applications where patterns of unknown or varying duration must be recognized online in data streams. Modern data stream processing frameworks are ubiquitously used to process high volumes of data, and adaptive memory and CPU allocation, facilitated by Progressive Window Widening, is crucial for their performance.