Diffusion kernel algorithms are interesting tools for distributed nonlinear estimation. However, for the sake of feasibility, it is essential in practice to restrict their computational cost and the number of communications. In this paper, we propose a censoring algorithm for adaptive kernel diffusion networks based on random Fourier features that locally adapts the number of nodes censored according to the estimation error. It presents fast convergence during the transient phase and a significant reduction in the number of censored nodes in the steady state, thus reducing the energy consumption and the computational cost mainly by decreasing the amount of communication between nodes. Simulation results show that the proposed technique can significantly decrease the computational cost with less impact on the convergence rate when compared to existing solutions.