  We show that the Nielsen-Olesen instability of the Savvidy vacuum with a
homogeneous chromomagnetic condensation disappears in the framework of the
functional renormalization group. This result follows from our observations:
(i) the vanishing imaginary part of the effective average action is realized
for arbitrary infrared cutoff as a novel fixed point solution of the flow
equation for the complex-valued effective average action and (ii) an
approximate analytical solution for the effective average action is obtained
without the pure imaginary part for large infrared cutoff. This result suggests
that there exists a physical mechanism for maintaining the stability or staying
on the fixed point even for sufficiently small infrared cutoff. We argue that
dynamical gluon mass generation (related to two-gluon bound states identified
with glueballs) occurs due to the Becchi-Rouet-Stora-Tyutin-invariant vacuum
condensate of mass dimension two without causing instability.
