InfluxDB came to mind because it focuses on storing time-series data. There is also TrailDB which was recently released by AdRoll but may not fit your use case as well.
In general, I would think about appending these messages to a log like Apache Kafka or RabbitMQ, and then creating subscribers/consumers which store that data in special purpose databases like InfluxDB. This allows for more flexibility as your application grows. Consider the following diagrams:
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