Yes, the sentence is grammatically correct. It conveys the idea that, regardless of human flaws or failings, God's nature remains constant and He continues to be faithful.
Possible rephrasing could include:
1. "God remains God, and He is faithful even in the face of our shortcomings."
2. "No matter our imperfections, God is still God and remains faithful."
3. "Despite our weaknesses, God is unchanging and faithful."