  During big bang nucleosynthesis, any injection of extra neutrons around the
time of the $^7$Be formation, i.e. at a temperature of order $T \simeq 50$~keV,
can reduce the predicted freeze-out amount of $^7$Be + $^7$Li that otherwise
remains in sharp contradiction with the Spite plateau value inferred from the
observations of Pop II stars. However, the growing confidence in the primordial
D/H determinations puts a strong constraint on any such scenario. We address
this issue in detail, analyzing different temporal patterns of neutron
injection, such as decay, annihilation, resonant annihilation, and oscillation
between mirror and standard model world neutrons. For this latter case, we
derive the realistic injection pattern taking into account thermal effects
(damping and refraction) in the primordial plasma. If the extra neutron supply
is the sole non-standard mechanism operating during the BBN, the suppression of
lithium abundance below Li/H~$\leq 1.9 \times 10^{-10}$ always leads to the
overproduction of deuterium, D/H~$\geq 3.6 \times 10^{-5}$, well outside the
error bars suggested by recent observations.
