Well according to imgur:
As long as images are getting at least 1 view every 6 months, they will stick around forever. After that, your image may be removed to create more space for newer images.
But the answer you linked to was only posted in March so it's guaranteed to have had at least one view in the past 6 months.
It's obviously not ideal if graphics for things go missing after 6 months and it's unacceptable if they go missing before that [predictable] deadline.
Ideally the SE sites would host the images themselves but as you can probably understand, this would essentially require them to create their own content delivery network to handle the extra disk and bandwidth requirements. Either that or they come to an arrangement with imgur where they guarantee lifetime hosting of all files.
I'm going to convert this into a bug to get more attention for it because if things carry on like this, it's going to be a serious issue for a lot of posts.
Edit: I have contacted imgur via email to ask them to investigate what happened in this specific case and to make sure, if it's a bug, it doesn't happen again. Hopefully it's a temporary issue.
Edit 2: Had a response back from the founder of Imgur saying they're investigating and fixing things. Rock on.
Edit 3: Should be completely fixed now and here's what happened:
I'm really sorry about that. Every
single missing image that occurred
from it is back online. It happened
with images that were under the
i.imgur.com domain, non of which were
deleted, but they weren't where they
were supposed to be.
Allow me to explain what happened and
how it's been fixed. We've been moving
data between disks (almost 45 million
images) over the past month because
the original storage we've been using
has been filling up rapidly. To move
all the images over to a new storage
solution, a script was created that
simply moves the images and creates
symlinks pointing to the new
locations. However, in order to resume
the script where it left off, it
ignored all symlinks it came across
and only moved actual images. All of
this has been working great and I've
been running it since early last
Last week when I moved all of SE's
images to the new setup
(stack.imgur.com), I did a similar
process with moving the file and
dropping down a symlink where it used
to be, that points to the new
location. This also worked great and
everything was moved over. However,
when you combine this with the general
image moving script that was already
running, it ends up ignoring all of
SE's symlinks and images that were
just working fine are no longer
linking up properly.
To fix this, I've changed the image
moving script to take SE's symlinked
images into account and handle them
appropriately. I've also just finished
scanning SE's entire library of images
to make sure that each and every one
was in the proper place and
accessible. I've also setup additional
monitoring for 404's on the
stack.imgur.com, to ensure that
something like this never happens with
the new system.
If you have any
please let me know. I also contacted
Jeff and the sysadmins for SE and
informed them of the fix as well.