Software aging is a phenomenon of progressive degradation of software execution environment caused by software faults. In this paper, we propose software life-extension as an operational countermeasure against software aging and present the mathematical foundations of software life-extension by means of stochastic modeling. A semi-Markov process is used to capture the behavior of a system with software life-extension and to analyze the system's availability and completion times of jobs running on it. The semi-Markov process can correctly model the time-based life-extension and allows us to derive the optimal trigger for starting life-extension in terms of system availability and mean job completion time. We also present an effective combination of software life-extension and software rejuvenation that can maximize the system availability compared with a system using either rejuvenation or software life-extension.