We investigate massive supersymmetric (SUSY) Higgs theories with real matter fields in two and three space-time dimensions. An exact expression for the nonperturbative correction to the vacuum energy density due to a dilute instanton gas is obtained. The first quantum correction vanishes identically, whereas the second correction is found to be negative definite for a specific two-dimensional theory. Consequently in general dynamical breakdown of the SUSY algebra due to vacuum tunneling takes place in two and three space-time dimensions. It is shown that there exists a nonzero leakage of SUSY flux which is proportional to the volume of space-time. The resulting boson-fermion mass splitting is calculated.