We store the call recordings up to 6 months (180 days) from the day of the call. This means you can listen/stream and download the call recordings from your Exotel dashboard for up to 6 months. After 6 months, the entry in your inbox will be intact but the recordings won't be available for download.
Also, we would suggest bulk download the recordings and store them on your Server/Computer. You can refer to this article for the same "How do I download all recordings?".