Many times he delivered them,
but they were rebellious in their purposes
and were brought low through their iniquity.
Nevertheless, he looked upon their distress,
when he heard their cry.
God is faithful, even when we are not. That is what this psalm sings about with praise. It is one of a series of psalms that recounts Israel's history, which is mostly a record of willful disobedience to God, disregard for His Law, spectacular failure of leaders and kings, intervening judgment, and most of all, God's overwhelming forgiving love when they cried out to Him again.
This verse says Israel was delivered many times. That is true. The exodus was just the beginning of God's rescue of His people. He did it time and time again, even as they slipped into idolatry with fresh memories of Egyptian slavery still with them. A band of people who watched God drown Pharaoh's army in the Red Sea quickly turned from worshiping Him. That experience IS the constant stream of Old Testament narrative over generations. Many times they sinned. Many times they were rebellious. Many times they failed at keeping the Law of the Lord. Many times their iniquities brought them low... and many times God delivered them again.
God did this because He "remembered his covenant" (Psalm 106:45) more than their imcompentence at keeping it. "For their sake" God delivered them and "relented according to the abundance of his steadfast love" (also found in Psalm 106:45). He delivered them for His sake. For His faithfulness to His covenant out of His faithful, holy, consistent, merciful grace God saves His people.
Your steadfast, faithful love is still known in Your saving work. In Christ I am forever delivered, not because I am so good, but because You loved me in Your Son. My record of rebellion and failure brings me low in my iniquity, no better than an Israelite idolater dancing before a golden calf. But it is all Your work to save me in Your Son, and I keep throwing my soul by faith into that amazing grace and work that He has done for me!