More Grace?

An interesting question was raised at last night's Bible study (Hebrew 11).  We were talking about how all of the saints of the Old Covenant had lived by faith, as we do today, and that our faith is a response to the grace of God.  If God did not offer us grace, we would not be able to respond in faith {What would we respond to without God's offer of forgiveness?}.  The question was asked, if some people don't respond, why doesn't God just give them more grace until they do?  The question gets to the heart of the relationship between a holy omnipotent God and his fallen freewill creation.
How much grace is enough?  Do we have the right to ask God for more grace? {Grace being an undeserved gift, it seems rather cheeky of us to ask God for more, but when those who refuse God's call are our own relatives or friends our desperation is certainly understandable}
I'm not a full T.U.L.I.P. Calvinist (you can look it up if you want) because I don't believe in Irresistible Grace (or Limited Atonement).  When reading the Bible I see a lot of people to whom God holds out his hands in hope only to see them refuse to accept him.  As God says of his chosen people in Isaiah, "All day long I have held out my hands to an obstinate people" (Isaiah 65:2a).  Time and time again the Lord pleads with his people to repent and return to him.  He sends them prophets to warn them, he shows them miracles as proof, he tries tough love by judging their sins; often to no avail.  It seems clear that God wants everyone to repent and be saved but it blocked by our willful rebellion which refuses to admit our own wrongs or seek help from above.
In the end, God will decide who receives one chance at salvation, and who receives many.  It is not for me to say that anyone is beyond redemption or that it is too late for anyone on this side of the grave.  I simply know that God wants us to receive Jesus Christ, to be cleansed of our sins, and to once again have fellowship with our heavenly father.  Peter wrote about God's patience (he would certainly know having needed it on many occasions), "The Lord is not slow in keeping his promise, as some understand slowness.  He is patient with you, not wanting anyone to perish, but everyone to come to repentance." (II Peter 3:9).
Any Bible study that leads us to contemplate the depth of God's love and mercy is time well spent.