I just changed my avatar,,no waiting at all, it showed up right away.
Sometimes, depending on browser settings you may have to hold down the shift key when you refresh or reload a page to get changes to show up. I don't think that is your problem though, as I see no avatar photo either.
I noticed that your profile pic is 250 pixels wide, the avatar pic is not supposed to be more than 200. In my settings page where I upload a pic it says "image scale" is turned on (I see no way to turn it on or off, must be a admin function)and it automatically re-sizes the images,it seems to work for me as I just tested it with a 250 pixel wide photo. Does your page say "image scale" is on?
When you upload the avatar, does it show up on the upload page?
Maybe it will show up after a while,,, but I do not have to wait any amount of time. It seems strange it would be different for you.