Please go back and read ALL of chapter 9, and maybe even ALL of Romans. Read what Paul says - his entire argument.
I have read it...many times.
Paul is very strong on God's sovereignty...that's one reason he emphasized predestination in Egph 1. Another reason is for the saints' assurance. Salvation does not depend on what they've done...if that was so they could disbelieve as well as believe their own way into Heaven. Faith is from God as Paul discovered when Jesus knocked him from His horse to convince him of truth. When God grants faith, He never removes it. A saint is granted by God to remain in Heaven forever.
This post sent me into fits of laughter earlier today. Every single Calvinist I know - every single one - can quote Romans 9 from memory.