  The effect of self-irradiation damage can influence many properties of a
radioactive material. Actinide materials involving the decay through alpha
radiation have been frequently studied using techniques such as transport,
thermodynamics, and x-ray diffraction. The use of nuclear magnetic resonance
(NMR) spectroscopy to study such effects, however, has seen relatively little
attention. Here, we use $^{239}$Pu NMR to study the local influence of
self-damage in a single crystal of the candidate topological insulator
plutonium tetraboride (PuB$_{4}$). We first characterize the anisotropy of the
$^{239}$Pu resonance in a single crystal and confirm the local axial site
symmetry inferred from previous polycrystalline measurements. Aging effects are
then evaluated over the timeframe of six years. We find that, though the static
NMR spectra may show a slight modulation in their shape, their field-rotation
pattern reveals no change in Pu local site symmetry over time, suggesting that
aging has a surprisingly small impact on the spatial distribution of the static
hyperfine field. By contrast, aging has a prominent impact on the NMR
relaxation processes and signal intensity. Specifically, aging-induced damage
manifests itself as an increase in the spin-lattice relaxation time $T_{1}$, an
increased distribution of $T_{1}$, and a signal intensity that decreases
linearly by 20 % per year. The spin-spin relaxation time $T_{2}$ in the aged
sample shows a strong variation across the spectrum as well as a drastic
shortening towards lower temperature, suggesting growth of slow fluctuations of
the hyperfine field that are linked to radiation-damage-induced inhomogeneity
and could be responsible for the signal wipeout that develops over time.
