SoS are an ensemble of complex systems, which have the potential for an extraordinary amount of structural complexity, even temporarily, as a result of interconnections and couplings that can vary in strength. Because of this, SoS can be vulnerable to sudden catastrophic collapse as a result of small and insignificant partial functionality losses in one of the constituent systems. This paper provides an analysis of the response SoS to uncertainties in the form of partial failures, which is complemented by the presentation of a measure of structural complexity for SoS. Experiments with the development of random graphs to simulate SoS show that a partial failure initiated in one system has a high possibility of leading to a collapse of another system of SoS, sometimes even before leading to total failure in the originating system. After pinpointing the effect of the complexity of today's system of systems (SoS), we present a first-step understanding of why unanticipated failures find more potential and more pathways to their occurrence when interventions in SoS operations, standards or processes are conducted without enough insight and without consideration of the fundamental nature of complexity. We then demonstrate a condition where the incremental changes actually lead to failure of the SoS to meet its performance parameters.