seems like it is only capturing the first frame of the gif, maybe the second as well.
That would explain why the others didn't work. Looks like the tink is probably only 2 frames and the other are 3 or more.
I dont know anything about Imagemagick, but can you change the setting for quality to 100% for thumbnails and see if that makes a difference?
Only thing I can think of, have no other ideas why.