We investigate vegetation uprooting by flow for Avena sativa seedlings with stem-to-sediment size ratio close to unity and vanishing obstacle-induced scouring. By inducing parallel riverbed erosion within an experimental flume, we measure the time-to-uprooting in relation to root anchoring and flow drag forces. We link the erosion rate to the uprooting timescales for seedlings with varying mean root length. We show that the process of continuous erosion leading to uprooting resembles that of mechanical fatigue where system collapsing occurs after a given exposure time. By this analogy, we also highlight the nonlinear role of the residual root anchoring versus the flow drag acting on the canopy when uprooting occurs. As a generalization, we propose a framework to extend our results to time-dependent erosion rates, which typically occur for real river hydrographs. Finally, we discuss how the characteristic timescale of plant uprooting by flow erosion suggests that vegetation survival is conditioned by multiple erosion events and their interarrival time.