In this paper, we study a highly generic version of influence maximization (IM), one of optimizing influence campaigns by sequentially selecting " spread seeds " from a set of candidates, a small subset of the node population, under the hypothesis that, in a given campaign, previously activated nodes remain " persistently " active throughout and thus do not yield further rewards. We call this problem online influence maximization with persistence. We introduce an estimator on the candidates' missing mass – the expected number of nodes that can still be reached from a given seed candidate – and justify its strength to rapidly estimate the desired value. We then describe a novel algorithm, GT-UCB, relying on upper confidence bounds on the missing mass. We show that our approach leads to high-quality spreads on classic IM datasets, even though it makes almost no assumptions on the diffusion medium. Importantly, it is orders of magnitude faster than state-of-the-art IM methods.