Software systems are made to evolve in response to changes in their contexts and requirements. As the systems evolve, security concerns need to be analysed in order to evaluate the impact of changes on the systems. We propose to investigate such changes by applying a meta-model of evolving security requirements, which draws on requirements engineering approaches, security analysis, argumentation and software evolution. In this paper, we show how the meta-model can be instantiated using a formalism of temporal logic, called the Event Calculus. The main contribution is a model based approach to argument analysis, supported by a tool which generates templates for formal descriptions of the evolving system. We apply our approach to several examples from an Air Traffic Management case study.