Long ties, the social ties that bridge different communities, are widely believed to play crucial roles in spreading novel information in social networks. However, some existing network theories and prediction models indicate that long ties might dissolve quickly or eventually become redundant, thus putting into question the long-term value of long ties. Our empirical analysis of real-world dynamic networks shows that contrary to such reasoning, long ties are more likely to persist than other social ties, and that many of them constantly function as social bridges without being embedded in local networks. Using a novel cost-benefit analysis model combined with machine learning, we show that long ties are highly beneficial, which instinctively motivates people to expend extra effort to maintain them. This partly explains why long ties are more persistent than what has been suggested by many existing theories and models. Overall, our study suggests the need for social interventions that can promote the formation of long ties, such as mixing people with diverse backgrounds.