As Constantine wrote you can run an Org Babel snippet to fetch the image from the remote server with
wget and display link the local copy of the image. This leaves you with the problem that the snippet would only be run once unless you force re-evaluation.
An out-of-emacs solution is to set up a cron job or similar to repeatedly fetch the image from the remote and overwrite a well-known file which would be linked in your org file. That too seems ugly to me, though.
A cleaner solution would be to write a function that fetches the image and then redisplays inline images in one go. You could then simply run the function to update the status image on demand.
Something along these lines:
(defun update-my-pic (url filename)
(shell-command (concat "wget -O " filename " " url))
(update-my-pic "https://www.gravatar.com/avatar/d593a36fb27c41445fade43a1fdd632c" "~/tmp/pic.png")
(update-my-pic "https://www.gravatar.com/avatar/917480313534cf1fd09009e861a2c52d" "~/tmp/pic.png")
This would update a picture link to a file "~/tmp/pic.png".