  We investigate the phenomenological viability of a recently proposed class of
composite dark matter models where the relic density is determined by 3 to 2
number-changing processes in the dark sector. Here the pions of the strongly
interacting field theory constitute the dark matter particles. By performing a
consistent next-to-leading and next-to-next-to-leading order chiral
perturbative investigation we demonstrate that the leading order analysis
cannot be used to draw conclusions about the viability of the model. We further
show that higher order corrections substantially increase the tension with
phenomenological constraints challenging the viability of the simplest
realisation of the strongly interacting massive particle (SIMP) paradigm.
