We consider highly dynamic distributed systems modelled by time-varying graphs (TVGs). We first address proof of impossibility results that often use informal arguments about convergence. We provide a general framework that formally proves the convergence of the sequence of executions of any deterministic algorithm over TVGs of any convergent sequence of TVGs. Next, we focus of the weakest class of long-lived TVGs, i.e., the class of TVGs where any node can communicate any other node infinitely often. We illustrate the relevance of our result by showing that no deterministic algorithm is able to compute various distributed covering structure on any TVG of this class. Namely, our impossibility results focus on the eventual footprint, the minimal dominating set and the maximal matching problems.