Manufacturer usually prepare one kernel which barely works and in many cases they don't cooperate with community. (Then they move to new board). Code hasn't been up-streamed, probably nobody is working any more on this, so new kernel can't exists. That's all we got.
But.
There is a community effort to bring mainline Linux to those devices. A10/20 is working fine, but they are old chips. H3 just arrived and I haven't see any progress since then.
http://linux-sunxi.org/Linux_mainlining_effort
There is also no sign of it in u-boot.