  We investigate the long-term dynamical survival of Earth co-orbital
asteroids, focusing on near-circular, near-planar orbits which existing studies
suggest are the most stable. Through numerical integration of test particles we
show that about a quarter of an initial population can survive for at least
50\% of the age of the solar system with horseshoe particles being four to five
times more likely to survive than L4/L5 Trojans. From the end state statistics
we constrain the existence of planetesimal-sized objects originally in
co-orbital libration, finding that typically $5^{-2}_{+7}$ such planetesimals
and no more than $27^{-9}_{+30}$ (95\% confidence) could have been present. Our
simulations also suggest that episodic variations in the terrestrial orbital
eccentricity may have caused bulk escape of co-orbitals, though variations
large enough ($>$0.01) to generate such episodes are statistically unlikely. We
then consider the orbital evolution of co-orbital asteroids of sizes down to $D
= 50$ m under the Yarkovsky effect and find that objects with $D$ $<$ 1 km
should escape over 4 Gyr with the smallest asteroids escaping after 200 Myr.
Further, we test whether Earth's co-orbital region may be populated by
asteroids arriving via outward Yarkovsky drift, as conjectured by Zhou et
al.~(A\&A, 622, A97, 2019). We find this is an inefficient process, as
planetary close encounters rapidly scatter the orbits far from Earth's and
towards the asteroid belt. Finally, we discuss how the destabilising action of
Yarkovsky may be mitigated through spin state evolution or late collisional
comminution of large parent asteroids.
