Online video websites receive huge amount of videos daily from users all around the world. How to provide valuable recommendations to viewers is an important task for both video websites and related third parties, such as search engines. Previous work conducted numerous analysis on the view counts of videos, which measure a video's value in terms of popularity. However, the long-lasting value of an online video, namely longevity, is hidden behind the history that a video accumulates its "popularity" through time. Generally speaking, a longevous video tends to constantly draw society's attention. With focus on one of the leading video websites, Youtube, this paper proposes a scoring mechanism quantifying a video's longevity. Evaluating a video's longevity can not only improve a video recommender system, but also help us to discover videos having greater advertising value, as well as adjust a video website's strategy of storing videos to shorten its responding time. In order to accurately quantify longevity, we introduce the concept of latent social impulses and how to use them measure a video's longevity. In order to derive latent social impulses, we view the video website as a digital signal filter and formulate the task as a convex minimization problem. The proposed longevity computation is based on the derived social impulses. Unfortunately, the required information to derive social impulses are not always public, which makes a third party unable to directly evaluate every video's longevity. To solve this problem, we formulate a semi-supervised learning task by using part of videos having known longevity scores to predict the unknown longevity scores. We propose a Gaussian Random Markov model with Loopy Belief Propagation to solve this problem. The conducted experiments on Youtube demonstrate that the proposed method significantly improves the prediction results comparing to baselines.