Since a few days, WhatsApp allows to download deleted media from their servers again. This automatically translates in the fact that WhatsApp continues to store our media on their servers also after downloading them.
This feature was partially available before: undownloaded media were available for 30 days and, when the recipient downloaded the media, WhatsApp immediately deleted it from the server.
Recently, WhatsApp has modified this behavior: when a media is successfully downloaded, WhatsApp doesn’t delete it from the server, allowing the users to download it again if the file was accidentally deleted in the path where WhatsApp saves media (sdcard/WhatsApp/).

In according to our recent tests, we have successfully downloaded images and videos received 2 months ago on the 2.18.113 version (presenting an error, but after that the image was correctly downloaded), and 3 months ago (we had to try multiple times in order to successfully redownload it).
With very old media (for example with images sent on last August 2017) it doesn’t seem possible, because WhatsApp asks us to request to the sender to send the media again in order to get it back.
In order to request to download the deleted media, it’s very important that we didn’t delete the message in WhatsApp, otherwise it won’t be possible.
Only if the file has been deleted in sdcard/WhatsApp/ and you have the message in the chat, you can successfully download it again.
Media files continue to be end-to-end encrypted also if WhatsApp doesn’t delete them from the server, so there’s anything to worry about.
The feature doesn’t seems to be available for iOS users, probably because the directory where WhatsApp saves media isn’t easily accessible, so this problem does not occur for them.