"Astatine is a fast-decaying, and therefore rare element. It has been estimated that in the Earth's crust there is no more than one tablespoon of astatine."
From the wiki:
"All of astatine's isotopes are short-lived; the most stable is astatine-210, with a half-life of 8.1 hours."
From the abstract:
An α-particle energy of 7750(20) keV and a half-life of 1.0 (+1.4,−0.4) ms were measured [for the new isotope astatine-190].
Now that's an unstable isotope! Makes astatine-210 look like Methuselah. Yet this is far from the fastest-decaying isotope known. Take a look at the exotic isotopes of helium:
https://en.wikipedia.org/wiki/Isotopes_of_helium#Heavier_hel...
The shortest-lived isotope is helium-10 with a half-life of 260(40) yoctoseconds.
If you don't have your exotic SI orders-of-magnitude prefixes memorized, you'll need a trip to this table to understand how incredibly short a yoctosecond is:
https://en.wikipedia.org/wiki/Orders_of_magnitude_(time)#Les...
That's why atoms stable atoms have a near balanced number of protons and neutrons, that only slowly gets pushed into the "more neutrons" direction as they grow.
There is also a proton drip line, where nuclei can decay from their ground state by proton emission. This would be slower as the proton must surmount a potentiel barrier, just like an escaping alpha particle does in nuclei that can undergo alpha decay.
https://upload.wikimedia.org/wikipedia/commons/thumb/6/65/De...