In recent years, the study of models and questions related to Liquid Democracy has been of growing interest among the community of Computational Social Choice. A concern that has been raised by practitioners is that the current academic literature focuses solely on static inputs, concealing a key characteristic of Liquid Democracy: the right for a voter to change her mind as time goes by. Our work initiates the incorporation of a time-horizon into decision-making problems in Liquid Democracy systems. Our approach, via a computational complexity analysis, exploits concepts and tools from temporal graph theory.