  The Hamiltonian Mean Field (HMF) model has a low-energy phase where $N$
particles are trapped inside a cluster. Here, we investigate some properties of
the trapping/untrapping mechanism of a single particle into/outside the
cluster. Since the single particle dynamics of the HMF model resembles the one
of a simple pendulum, each particle can be identified as a high-energy particle
(HEP) or a low-energy particle (LEP), depending on whether its energy is above
or below the separatrix energy. We then define the trapping ratio as the ratio
of the number of LEP to the total number of particles and the
``fully-clustered'' and ``excited'' dynamical states as having either no HEP or
at least one HEP. We analytically compute the phase-space average of the
trapping ratio by using the Boltzmann-Gibbs stable stationary solution of the
Vlasov equation associated with the $N \to \infty$ limit of the HMF model. The
same quantity, obtained numerically as a time average, is shown to be in very
good agreement with the analytical calculation. Another important feature of
the dynamical behavior of the system is that the dynamical state changes
transitionally: the ``fully-clustered'' and ``excited'' states appear in turn.
We find that the distribution of the lifetime of the ``fully-clustered'' state
obeys a power law. This means that clusters die hard, and that the excitation
of a particle from the cluster is not a Poisson process and might be controlled
by some type of collective motion with long memory. Such behavior should not be
specific of the HMF model and appear also in systems where {\it itinerancy}
among different ``quasi-stationary'' states has been observed. It is also
possible that it could mimick the behavior of transient motion in molecular
clusters or some observed deterministic features of chemical reactions.
