For effective social media marketing, identifying stable influencers-those who sustain their influence over an extended period-is more valuable than focusing on users who are influential only temporarily. This study addresses the challenge of distinguishing stable influencers from transient ones among users who are influential at a given point in time. We particularly focus on two distinct types of influencers: source spreaders, who widely disseminate their own content, and brokers, who play a key role in propagating information originating from others. Using six months of retweet data from approximately 19,000 Twitter users, we analyze the characteristics of stable influencers. Our findings reveal that users who have maintained influence in the past are more likely to continue doing so in the future. Furthermore, we develop classification models to predict stable influencers among temporarily influential users, achieving an AUC of approximately 0.89 for source spreaders and 0.81 for brokers. Our experimental results highlight that current influence is a critical factor in classifying influencers, while past influence also significantly contributes, particularly for source spreaders.