A typical inflatable reflector for space application consists of two thin membranes with a parabolic shape. It is critical to understand the interaction of the inflatable and the micrometeoroid environment to which it is exposed. This interaction leads to a series of penetrations of the inflatable membrane on the entrance and exit of the impacting particle, creating a pathway for gas to escape. To increase the fidelity of the of the estimated damage that will be incurred, we examine the literature for descriptions of micrometeoroid fragmentation and present a theoretical formulation for the damage caused by an impacting particle to the entrance and exit membranes. This theory is compared with an initial set of hyper-velocity tests for micrometeoroid-sized particles on thin film membranes. We use the results of these tests to produce a predictive model. This model is applied to estimate the damage rate near the 1 AU location and output predictions for the effectiveness of a micrometeoroid shield to reduce the damage on the lenticular and effectively optimize its lifetime. Finally, we apply the kinetic theory of gasses to develop expressions for the expenditure of gas over a specified mission lifetime due to penetrations. Although we examine the specific case of an inflated lenticular protected by extra membrane layers, our predictive model can be applied to any gossamer structure composed of polyimide membranes.