  The effect of the inclusion of ground state correlations into the QRPA
equation of motion for the two-neutrino double beta ($\beta\beta_{2\nu}$) decay
is carefully analyzed. The resulting model, called renormalized QRPA (RQRPA),
does not collapse near the physical value of the nuclear force strength in the
particle-particle channel, as happens with the ordinary QRPA. Still, the
$\beta\beta_{2\nu}$ transition amplitude is only slightly less sensitive on
this parameter in the RQRPA than that in the plain QRPA. It is argued that this
fact reveals once more that the characteristic behaviour of the
$\beta\beta_{2\nu}$ transition amplitude within the QRPA is not an artifact of
the model, but a consequence of the partial restoration of the spin-isospin
$SU(4)$ symmetry. It is shown that the price paid for bypassing the collapse in
the RQRPA is the violation of the Ikeda sum rule.
