I keep committing the same sin over and over - is God out of patience with me

If repeated failure disqualified people, Scripture would be a very short book. Peter denied Jesus three times in one night after swearing he never would - and Jesus met him afterward with breakfast and restoration, not expulsion (John 21:15-17). The command to forgive 'seventy times seven' (Matthew 18:22) describes God's own heart before it describes our duty, and 'His compassions fail not. They are new every morning' (Lamentations 3:22-23) was written for exactly this cycle.

A just man 'falleth seven times, and riseth up again' (Proverbs 24:16) - the rising is the faith part. But God's patience is not a license to stop fighting: grace teaches us to deny ungodliness (Titus 2:11-12). So change the strategy, not just the resolve: confess to a trusted believer instead of failing privately forever ('Confess your faults one to another... that ye may be healed', James 5:16), remove the access points ruthlessly (Matthew 5:29-30 is about severity toward occasions of sin), replace the habit rather than only resisting it (Romans 12:21 - overcome evil with good), and expect a war, not a single battle (Galatians 5:17).

The presence of the struggle is evidence of life - dead things do not fight. 'He which hath begun a good work in you will perform it until the day of Jesus Christ' (Philippians 1:6).