Why do we break promises? We break them because we change, or circumstances do. That is, we make a promise in one mood; the mood shifts, and we break it. Or we make a promise, but it isn't of much weight to us, so we let it slip. Or we make a promise, then sin grips us and the promise becomes inconvenient and burdensome, so we drop it to cling to our sin.
Why does God never break promises? He never changes, and He controls circumstances.
Put it another way: at any point, God knows Himself exhaustively, and knows all circumstances in all time-frames exhaustively. The latter actually springs from the former.
Thus it literally is not possible that God should ever be caught short by either a change in Himself, or in circumstances. He is the Lord, and He does not change (Malachi 3:6; cf. Hebrews 13:8). He works all things after the counsel of His will (Ephesians 1:11). The categories that produce faithlessness in us simply are not meaningful to God.
I see three immediate implications:
First, the believer can rest unreservedly on God's word of promise. Christ says He'll never cast us out, and He won't (John 6:37). God promises that all things will work together for our good, and they will (Romans 8:28). Jesus promises that not one of His sheep will perish, and they won't (John 10:28).
Second, the unbeliever needs to deal with the complete hopelessness of his situation, as matters stand. God promises to judge all secrets in the day of judgment (Ecclesiastes 12:23). He promises that all artifices of human pride and rebellion — all rationalizations, excuses, and dodges — will be swept away like so many cobwebs (Isaiah 2:11; 1 Corinthians 2:19). He promises that every knee will bow, and every tongue admit that Jesus is Lord, and they will (Philippians 2:10-11). Confess the truth now, to your salvation, or you will surely confess it in that day, to your damnation.
Third, the believer needs to take God as his model. I imagine many in unrepented sin read the start of the post and thought "Yes! That's why I had to change my mind! Situations changed!"
Not so fast, Turbo.
The Israelites made a promise without a full knowledge of the facts (Joshua 9) — and God held them to it, regardless (2 Samuel 21). It is characteristic of the righteous man that he "swears to his own hurt and does not change" (Psalm 15:4).