One of the fundamental properties of biochemical networks in cells is the preservation of viability under conditions of stress and environmental perturbation. This requires that the system maintains coordination in the sense that a stable (time-dependent) state can form under such conditions. Although this property emerges from the characteristics of the constitutive enzymes, the general conditions that must be satisfied by a network to maintain a viable state are not known. The essential features of enzymatic reactions are saturation kinetics and a nonlinear dependency of reaction rate on metabolite concentration. For a simple branched system we derive sufficient conditions on these features that, if satisfied, imply that the resulting metabolic processes remain coordinated when the system is exposed to external perturbations of any type, amplitude, or frequency. Upon removal of the perturbation, the unperturbed state will be recovered. When the system does not satisfy the sufficient conditions, it is shown that coordination depends on the nature of the perturbing signals. Furthermore, once coordination is lost, it cannot be retrieved by removal of the perturbing force and therefore the system cannot settle to any finite state. These results are supported by numerical analysis using three types of external signals: namely, rectangular, sinusoidal, and noisy signals.