Why is astatine so radioactive?
I don't think there is an actual answer to that. What we know about the radioactivity is based mostly on empiric observation and quantum physics is still not able to give precise answers about the process of radioactive decay. 

A similar question could be asked about technetium: why is it unstable, even though it stands in the periodic table between stable elements? Probably it's a matter of their proton and neutron configuration that for some reason are particularly unstable compared to their neighbourhood, but there is still no equation capable of giving the half-life of an isotope.

This has already been discussed and probably we will have to wait until the atom nucleus is better studied before being able to answer this question.