Combinatorial property testing deals with the following relaxation of
decision problems: Given a fixed property and an input $f$, one wants
to decide whether $f$ satisfies the property or is `far' from satisfying
the property.
It has been shown that regular languages are testable,
and that there exist context free language which are not testable.
We show that there exists a language that is accepted by a
deterministic counter automaton for which any $1/25$-test requires
$\Omega(poly(\log{n}))$ queries.
Thus,
proving that even if we restrict ourselves to, perhaps the simplest possible
stack automaton model, we do not ensure testability.