Acoustic event classification (AEC) and acoustic event detection (AED) refer to the task of detecting whether specific target events occur in audios. As long short-term memory (LSTM) leads to state-of-the-art results in various speech related tasks, it is employed as a popular solution for AEC as well. This paper focuses on investigating the dynamics of LSTM model on AEC tasks. It includes a detailed analysis on LSTM memory retaining, and a benchmarking of nine different pooling methods on LSTM models using 1.7M generated mixture clips of multiple events with different signal-to-noise ratios. This paper focuses on understanding: 1) utterance-level classification accuracy; 2) sensitivity to event position within an utterance. The analysis is done on the dataset for the detection of rare sound events from DCASE 2017 Challenge. We find max pooling on the prediction level to perform the best among the nine pooling approaches in terms of classification accuracy and insensitivity to event position within an utterance. To authors' best knowledge, this is the first kind of such work focused on LSTM dynamics for AEC tasks.