We have carried out Very Large Array (VLA) continuum observations to study the variability of Sgr A* at 43 GHz (l = 7 mm) and 22 GHz (l = 13 mm). A low level of flare activity has been detected with a duration of 62 hr at these frequencies, showing the peak flare emission at 43 GHz leading the 22 GHz peak flare by 620-40 minutes. The overall characteristics of the flare emission are interpreted in terms of the plasmon model of van der Laan by considering the ejection and adiabatic expansion of a uniform, spherical plasma blob due to flare activity. The observed peak of the flare emission with a spectral index, v super(-a), of a= 1.6 is consistent with the prediction that the peak emission shifts toward lower frequencies in an adiabatically expanding self-absorbed source. We present the expected synchrotron light curves for an expanding blob, as well as the peak frequency emission, as a function of the energy spectral index constrained by the available flaring measurements in near-IR, submillimeter, millimeter, and radio wavelengths. We note that the blob model is consistent with the available measurements; however, we cannot rule out the jet of Sgr A*. If expanding material leaves the gravitational potential of Sgr A*, the total mass-loss rate of nonthermal and thermal particles is estimated to be ,2 x 10 super(-8) M sub( )yr super(-1). We discuss the implication of the mass-loss rate, since this value matches closely the estimated accretion rate based on polarization measurements.