  Spectral diffusion arising from $^{29}$Si nuclear spin flip-flops, known to
be a primary source of electron spin decoherence in silicon, is also predicted
to limit the coherence times of neutral donor nuclear spins in silicon. Here,
the impact of this mechanism on $^{31}$P nuclear spin coherence is measured as
a function of $^{29}$Si concentration using X-band pulsed electron nuclear
double resonance (ENDOR). The $^{31}$P nuclear spin echo decays show that
decoherence is controlled by $^{29}$Si flip-flops resulting in both fast
(exponential) and slow (non-exponential) spectral diffusion processes. The
decay times span a range from 100 ms in crystals containing 50% $^{29}$Si to 3
s in crystals containing 1% $^{29}$Si. These nuclear spin echo decay times for
neutral donors are orders of magnitude longer than those reported for ionized
donors in natural silicon. The electron spin of the neutral donors `protects'
the donor nuclear spins by suppressing $^{29}$Si flip-flops within a `frozen
core', as a result of the detuning of the $^{29}$Si spins caused by their
hyperfine coupling to the electron spin.
