The mesoscopic Stoner instability is interesting phenomenon of symmetry breaking in isolated metallic quantum dots which exists due to competition between the single-particle energy and
Heisenberg exchange interaction. To study this phenomenon in the presence of coupling to a reservoir we compute the spin susceptibility of electrons on the quantum dot for different values of tunnel coupling and temperature. Our results suggest the existence of \emph{the quantum phase transition} at the critical value of the tunneling coupling which is determined by the Stoner-enhanced exchange interaction. This quantum phase transition is manifestation of suppression of the Coleman-Weinberg mechanism of symmetry breaking by tunneling to the reservoir.