  We show that for the half-filled Kondo lattice model on the honeycomb lattice
a Kondo breakdown occurs at small Kondo couplings $J_k$ within the magnetically
ordered phase. Our conclusions are based on auxiliary field quantum Monte Carlo
simulations of the so-called composite fermion spectral function. Within a U(1)
gauge theory formulation of the Kondo model, it becomes apparent that a Higgs
mechanism dictates the weight of the resonance in the spectral function. For
the honeycomb lattice we observe that for small $J_k$ the quasiparticle pole
gives way to incoherent spectral weight but it remains well defined for the
square lattice. Our result provides an explicit example where the magnetic
transition and the breakdown of heavy quasiparticles are detached as observed
in Yb(Rh$_{0.93}$Co$_{0.07}$)$_2$Si$_2$ [Friedemann et al., Nat. Phys.
\textbf{5}, 465 (2009)].
