Paul has just made grandiose claims about the indomitable purposes of God in the life of the believer:
KJV Rom 8:31 What shall we then say to these things? If God be for us, who can be against us? Rom 8:32 He that spared not his own Son, but delivered him up for us all, how shall he not with him also freely give us all things? Rom 8:33 Who shall lay any thing to the charge of God's elect? It is God that justifieth. Rom 8:34 Who is he that condemneth? It is Christ that died, yea rather, that is risen again, who is even at the right hand of God, who also maketh intercession for us. Rom 8:35 Who shall separate us from the love of Christ? shall tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword? Rom 8:36 As it is written, For thy sake we are killed all the day long; we are accounted as sheep for the slaughter. Rom 8:37 Nay, in all these things we are more than conquerors through him that loved us. Rom 8:38 For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, Rom 8:39 Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.
This leads to the need to explain the apparent failure of God's purposes concerning Israel. He says the promises concerning Israel did not fail because only some of Israel count as Israel. The fall of the bulk of Israel does not constitute the failure of the promises toward the remnant because the purposes of God will be accomplished in the remnant:
Rom 9:6 Not as though the word (ie: promise) of God hath taken none effect. For they are not all Israel, which are of Israel: Rom 9:7 Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called. Rom 9:8 That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed. Rom 9:9 For this is the word of promise, At this time will I come, and Sara shall have a son. Rom 9:10 And not only this; but when Rebecca also had conceived by one, even by our father Isaac; Rom 9:11 (For the children being not yet born, neither having done any good or evil, that the purpose of God according to election might stand, not of works, but of him that calleth;) Rom 9:12 It was said unto her, The elder shall serve the younger. Rom 9:13 As it is written, Jacob have I loved, but Esau have I hated.
So what is the specific promise concerning Israel that he is assuring his readers will not fail to come to pass? And how does he prove that the promise has not and will not fail?