Any modern system writes events into files, called log files. Those contain crucial information which are subject to various analyses. Examples range from cybersecurity, intrusion detection over usage analyses to trouble shooting. Before data analysis is possible, desired information needs to be extracted first out of the semi-structured log messages. State of the art event parsing often assumes static log events. However, any modern system is updated consistently and with updates also log file structures can change. We call those changes 'mutations' and study parsing performance for different mutation cases. Latest research discovers mutations using anomaly detection post mortem, however, does not cover actual continuous parsing. Thus, we propose a novel, flexible parser, called FlexParser which can extract desired values despite gradual changes in the log messages. It implies basic text preprocessing followed by a supervised Deep Learning method. We train a stateful LSTM on parsing one event per data set. Statefulness enforces the model to learn log message structures across several messages. Our model was tested on seven different, publicly available log file data sets and various kinds of mutations. Exhibiting an average F1-Score of 0.98, it outperforms other Deep Learning methods as well as state-of-the-art unsupervised parsers.