By default, WhatsApp don’t provide option to save or download media status from your contacts.
You can only download your WhatsApp media status with the aide of an application.
Go to your Google Play Store search, download and install Status Saver for WhatsApp.
From the Status Saver for WhatsApp App you can view and download all your status that you’ve viewed. Note that only media status (images and videos) that you’ve viewed can only be seen and save from the app.