In this paper, we study a flexible routing strategy for demand protection and a corresponding optimization problem for networks that permanently experience fluctuations of the capacity available on their links. This is an important and novel topic as limited link availability is a fundamental feature of wireless networks; yet majority of work in survivable network design is restricted to total failures of single links. Hence, protection against partial failures of multiple links is considered as congestion avoidance. We assume a given finite set of network states. Each state is characterized by a vector of link availability coefficients specifying, for each link, the fraction of its nominal (maximum) capacity available in this state, and by a traffic coefficients vector specifying, for each demand, the proportion of its nominal traffic to be realized in the considered state. Our routing strategy allows for adjustment (thinning or thickening) of the reference path-flows. For a given nominal value x of a path-flow, its thickening is limited to Tx where T is a given constant greater than or equal to 1. Thus, in each state, the value of every path-flow can range from 0 to T times its reference value. It turns out that the corresponding link cost minimization problem (where link capacities and state-dependant path-flows are decision variables) is NP-hard. We present a non-compact linear programming formulation of the problem together with a solution algorithm based on path generation. We illustrate the effectiveness of the introduced routing strategy by presenting numerical results for a set of representative network examples.