For starters, any image over 125x125 is automatically resized, and the gif you posted was 500x200, so it'll trigger the reencoder. The reencoding process does not preserve anything in animated images other than the first frame, and this is intentional. That being said even if you did get it at or below 125x125 sometimes the upload security checks kick in and it sees it as a potential threat and it will either kick the image back as invalid, or will forcefully reencode it, again only preserving the first frame.
It's really just a trial and error process getting animated avatars working. I can't tell you exactly what you need to get one working as I've never really played with them and I've done everything I can outside of ripping out the forum avatar system and reworking it entirely to fix some of the buggy behavior.