My understanding of the relationship between works and salvation is that works are the inevitable fruit of salvation by grace (1 John 3:6, Matthew 7:16-18). And my understanding of perseverance is that the genuinely saved will persevere (Philippians 1:6, 1 John 2:19).
However, this passage from Galatians does not seem to fit cleanly with my understanding:
Galatians 6:8-9 (NASB)
8 For the one who sows to his own flesh will from the flesh reap corruption, but the one who sows to the Spirit will from the Spirit reap eternal life. 9 Let us not lose heart in doing good, for in due time we will reap if we do not grow weary.
Particularly in verse 9, Paul seems to be telling the Galatians to keep doing good in order to reap eternal life. Furthermore, it sounds like this "doing good" falls under human responsibility, or why would Paul need to admonish the Galatians to do so? That sounds a lot like works salvation.
How do those with understandings similar to mine explain/interpret this verse? How does the context shed light on this passage?