How do those who believe in salvation by grace, and in works being the fruit of salvation, explain Galatians 6:8-9? 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?
I think the key thing here is understanding what it means to "sow to flesh" and "sow to the Spirit".  

The difference (referencing Bob Utley's commentary) is the key difference between the two basic approaches to being right with God: our own effort, or God's free grace.  

The former (sowing to flesh) refers to trying to be right by God by trying to work for it.  The latter (sowing to the Spirit) refers to trying to be right by God through his free grace.  

In other words, Paul is strongly warning the Galatians to not attempt to be right with God through their own effort.  

In verse 9, he goes on to encourage the Galatians to continue in their works.  We are not saved by our works, but saved unto works.  You see this same thing in Ephesians 2:8-10: 


  For by grace you have been saved through faith. And this is not your
  own doing; it is the gift of God, not a result of works, so that no
  one may boast. 10 For we are his workmanship, created in Christ Jesus
  for good works, which God prepared beforehand, that we should walk in
  them.


So the interpretation here should be a strict admonition to not mock God by attempting to hold up your good works as a sign of your deserving eternal life, but rather that you would abandon your good works as an effort towards salvation, and instead, embrace good works gladly as a privilege given to those who have ceased their striving to be justified through those same good works.