We have carried out Very Large Array (VLA) continuum observations to study the variability of Sgr A* at 43 GHz (λ = 7 mm) and 22 GHz (λ = 13mm). Alow level offlare activity has been detected with a duration of ∼2hr at these frequencies, showing the peak flare emission at 43 GHz leading the 22 GHz peak flare by ∼20-40 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-α, of α = 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 × 10-8 M⊙ yr-1. We discuss the implication of the mass-loss rate, since this value matches closely the estimated accretion rate based on polarization measurements.