  The temperature dependence of the gapped triplet excitations (triplons) in
the 2D Shastry-Sutherland quantum magnet SrCu$_2$(BO$_3$)$_2$ is studied by
means of inelastic neutron scattering. The excitation amplitude rapidly
decreases as a function of temperature while the integrated spectral weight can
be explained by an isolated dimer model up to 10~K. Analyzing this anomalous
spectral line-shape in terms of damped harmonic oscillators shows that the
observed damping is due to a two-component process: one component remains sharp
and resolution limited while the second broadens. We explain the underlying
mechanism through a simple yet quantitatively accurate model of correlated
decay of triplons: an excited triplon is long-lived if no thermally populated
triplons are near-by but decays quickly if there are. The phenomenon is a
direct consequence of frustration induced triplon localization in the
Shastry--Sutherland lattice.
