Imgur is a great website for hosting images, but are they keeping those images forever?
If not, for how long?
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Stated by Imgur under Imgur help → Support → Images
How long do you keep the images?
Forever! An image is only removed if deletion is requested.
Imgur used to delete uploaded images that haven't got any views in six months: https://wayback.archive.org/web/20141212172016/http://imgur.com/faq#long
Since February 2015, when Imgur Pro service was discontinued, Imgur claims to preserve all images: https://blog.imgur.com/2015/02/09/imgur-pro-for-everyone/
On April 19, 2023, Imgur announced a policy change. Along with NSFW images being deleted, they will also start deleting images not tied to a user account on May 15, 2023.
So the answer is: Forever, but only if you uploaded it with a user account. Otherwise, it will eventually be deleted.