The breakdown of structure in gelled suspensions due to the application of an external stress results in flow. Here we explore the onset of flow by investigating the onset of nonlinear behavior in the elastic moduli of a widely studied class of thermo-reversible gels over a range of volume fractions. We employ the system composed of octadecyl-coated silica particles (radius = 24 nm) suspended in decalin that displays a transition from a liquid to a gel below a volume-fraction-dependent gel temperature, T-gel. The perturbative yield stress at which the gel modulus drops to 90% of its value in the linear viscoelastic limit is found to increase monotonically with volume fraction and decreasing temperature. The recently proposed activated barrier-hopping theory of Schweizer and co-workers(1,2) presents a framework to capture the impact of external forces on the mechanical properties of structurally arrested systems. By characterizing particle interactions with a Yukawa potential and employing the resultant static structure factor as input into the activated barrier-hopping theory, we make predictions for how the elastic modulus evolves with the applied stress. Comparisons of these calculations with experiments reveal that the theory does an excellent job of quantitatively capturing the perturbative yield stresses over the entire range of volume fractions and temperatures explored in the study. The match of predictions with experimental results suggests that the theory not only captures particle localization but also how this localization is modulated in the presence of an external stress.