The LORD says, "I will not break my covenant" (89:34), and the psalm says, "You have renounced the covenant of your servant" (89:39). Did God break his promise?

The psalm says both, and it says both to God. It doesn't soften either. The oath is the LORD's own words: "I will not break my covenant, nor alter what my lips have uttered. Once I have sworn by my holiness, I will not lie to David" (89:34-35). The lament is what the psalm sees: "You have renounced the covenant of your servant. You have defiled his crown in the dust" (89:39). The oath had said what would happen if David's children forsook the LORD's law: "then I will punish their sin with the rod, and their iniquity with stripes. But I will not completely take my loving kindness from him, nor allow my faithfulness to fail" (89:32-33). But the lament doesn't say that this had happened; from 89:38 to the end the psalm names no sin, and these notes don't supply one. What it does is hold the LORD to his word. Its last question turns the oath's own words back to him: "Lord, where are your former loving kindnesses, which you swore to David in your faithfulness?" (89:49). Within the psalm the question gets no answer. The next and last verse is "Blessed be the LORD forever more. Amen, and Amen" (89:52), one of the four closings the introduction divides the book at; the psalm doesn't say whether it is part of the psalm's own prayer or closes the book's third part.