Blogger Employee provided, in a forum thread, the answer to the question
Animated images won't stay animated if the image is a Blogger-hosted, since Picasa doesn't support animated images (and the Blogger-hosted photos are stored in Picasa Web Albums).
There is a workaround, which looks more complicated than it really is.
>> Forum thread links: bX-*00048
>> Copy this tag: bX-*00048