  Recent results on the dynamical stability of a system involving the
interaction of the ELKO spinor field with standard matter in the universe have
been reanalysed, and the conclusion is that such system does not exhibit
isolated stable points that could alleviate the cosmic coincidence problem.
When a constant parameter $\delta$ related to the potential of the ELKO field
is introduced in the system however, stable fixed points are found for some
specific types of interaction between the ELKO field and matter. Although the
parameter $\delta$ is related to an unknown potential, in order to satisfy the
stability conditions and also that the fixed points are real, the range of the
constant parameter $\delta$ can be constrained for the present time and the
coincidence problem can be alleviated for some specific interactions. Such
restriction on the ELKO potential opens possibility to apply the ELKO field as
a candidate to dark energy in the universe, and so explain the present phase of
acceleration of the universe through the decay of the ELKO field into matter.
