I am looking for the webpage of a video short that I saw several years
(Less than 5, more than 1) ago. I have visited the site before and
seen the video but since forgotten.

This is what I can remember:
-It was a 3D, rendered, animation
-Most of the creatures in the short were robotic forms of common animals
-The opening scene involved a robotic caterpillar on the leaves of a tree
-At some point later a robotic stork type animal flies away from the tree
-The stork is driven by a rocket
-The stork lands on a platform and is put to sleep by ball shaped
creatures that play a musical tune to knock out the stork

I think it may have been in the running for a Sundance Film Festival Award.
You could purchase the short as a DVD on the site.

Yeah, its weird, but it was good, so....

I am quite certain that you're describing a portion of Andy Murdock's
"Lots of Robots," a remarkable animated film in progress.

Here's a link to the segment with the caterpillar, the rocket-powered
bird, and the little ball-shaped critters:

Lots of Robots: LOR Volume One
http://www.lotsofrobots.com/Web3/MoviePlayMain/MovieDisplay/LOR_Play_V1_4.htm

In case you want to browse around the site, here's the homepage:

Lots of Robots
http://www.lotsofrobots.com

If you like "Lots of Robots," be sure to check out Andy's first short,
"Rocket Pants":

Lots of Robots: Rocket Pants
http://www.lotsofrobots.com/RPpage2.htm

My Google search strategy:

Google Web Search: "andy murdock" "lots of robots"
://www.google.com/search?hl=en&q=%22andy+murdock%22+%22lots+of+robots%22

I hope this is exactly what you were looking for! If it is not, or if
anything is unclear or incomplete, please request clarification; I'll
be glad to offer further assistance before you rate my answer.

Best regards,
pinkfreud

Practically an instant response and right on target!