During Old Testament times, the Holy Spirit interacted with people differently than He does now. Today, Christians are permanently indwelt by the Holy Spirit. During Old Testament times, the Holy Spirit indwelt people as needed. For example, there are several instances in the Old Testament where the Holy Spirit came upon a king, a prophet, or a judge to empower that person for special ministry. When the task was completed, the Holy Spirit would then depart from that person. For instance, Samson, the Old Testament judge, was empowered by the Holy Spirit in Judges 14:6 to slay a lion that was attacking him. Later in Judges 14:19, the Holy Spirit "came upon" Samson again so that he could bring God's wrath upon the Philistines. This shows us that the Holy Spirit would empower Samson to complete certain tasks and then depart. 

David relied on the empowerment of the Spirit to fufill his duties as Israel's king. Upon recognizing his sin, he simply asks God to allow the Spirit to continue to empower him for that task. Today, Christians are permanently indwelt by the Holy Spirit. This is one of the benefits and blessings of the New Covenant instituted by Jesus' death, burial, and resurrection.