  We consider the Hamiltonian version of a $\cal PT$-symmetric lattice that
describes dynamics of coupled pendula under a resonant periodic force. Using
the asymptotic limit of a weak coupling between the pendula, we prove the
nonlinear long-time stability of breathers (time-periodic solutions localized
in the lattice) by using the Lyapunov method. Breathers are saddle points of
the extended energy function, which are located between the continuous bands of
positive and negative energy. Nevertheless, we construct an approximate
Lyapunov function and estimate its evolution on a long but finite time
interval. The nonlinear stability analysis becomes possible for the $\cal
PT$-symmetric lattice only because of the existence of a Hamiltonian structure.
