We explore the fundamental limits on coherence preservation by dynamical decoupling methods in terms of control time scales and the spectrum/bandwidth of the environment. We focus on a decohering qubit controlled by arbitrary sequences of pi pulses. Using results from mathematical analysis, we establish a lower bound for coherence loss in terms of the minimum time between the pulses and the spectral cutoff frequency of the environment. We argue that similar bounds are applicable to a variety of open-loop unitary control methods while we find no explicit dependence of such lower bounds on the total control time. We use these findings to automatically generate "bandwidth adapted dynamical decoupling" sequences that can be used for preserving a qubit up to arbitrary times with the best fidelities theoretically possible given the available control capabilities. We also introduce "Walsh dynamical decoupling" schemes that are optimized for digital sequence generation. Our results imply that fact that, unlike in quantum fault-tolerant architecture, errors cannot be reduced indefinitely using reversible control methods yet a small error can be maintained for a long time.