  The acceptance-corrected dielectron excess mass spectra, where the known
hadronic sources have been subtracted from the inclusive dielectron mass
spectra, are reported for the first time at mid-rapidity $|y_{ee}|<1$ in
minimum-bias Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 and 200 GeV. The excess
mass spectra are consistently described by a model calculation with a broadened
$\rho$ spectral function for $M_{ee}<1.1$ GeV/$c^{2}$. The integrated
dielectron excess yield at $\sqrt{s_{NN}}$ = 19.6 GeV for $0.4<M_{ee}<0.75$
GeV/$c^2$, normalized to the charged particle multiplicity at mid-rapidity, has
a value similar to that in In+In collisions at $\sqrt{s_{NN}}$ = 17.3 GeV. For
$\sqrt{s_{NN}}$ = 200 GeV, the normalized excess yield in central collisions is
higher than that at $\sqrt{s_{NN}}$ = 17.3 GeV and increases from peripheral to
central collisions. These measurements indicate that the lifetime of the hot,
dense medium created in central Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV
is longer than those in peripheral collisions and at lower energies.
