Why is Astatine monoatomic?
One key problem with astatine is that it's incredibly unstable. There are no known stable isotopes, and the longest-lived has a half-life of ~8 hours. So no one has been able to (yet) prepare enough to make real measurements. Thus, we don't know for sure whether solid At is diatomic (like the other halogens) or monatomic.

On the other hand, high-level first-principals (quantum) calculations have been performed that suggest astatine has some unusual properties. The full paper by Roald Hoffmann and Neil Ashcroft at Cornell was published in 2013 in Phys. Rev. Lett.: "Condensed Astatine: Monatomic and Metallic" and also covered in multiple science news sites, including Chemistry World.

The calculations on At:


  predict that it will be a metallic solid. That’s perhaps not so surprising given that iodine, the halogen above it in the periodic table, is itself a dark silvery solid (although not truly metallic itself) and that astatine’s melting point is 302&deg;C. But the real surprise of the new results is that the solid wouldn’t be composed of diatomic molecules, like all the other halogens, but would be monatomic.


Why would At be different than solid $\ce{I2}$?


  ... The monatomic form appeared only with spin-orbit coupling included. "These effects influence the atoms’ propensity to form certain bonds and crystal structures, usually by reducing molecular binding energies," says Hermann. Earlier calculations have indicated that in the gas phase astatine would still form a weakly bound diatomic molecule.


In other words, it's the spin orbit coupling contribution of relativistic effects that would prevent the formation of diatomic molecules in solid At.