I don't think N. T. Wright solves the problem, but he at least acknowledges it. Wright asks, "What was impossible for the law? That it should give life. It offered it, but could not deliver" ("Romans," NIB 577). He then says,
It could not do so because it was "weak because of the flesh." Despite many commentators and preachers who have been eager to see Paul say negative things about the law, he declares, summing up the argument of chap. 7, that there was nothing wrong with it in itself. The problem lay elsewhere: in the "flesh"—not the physicality of human nature, which was God-given and will be reaffirmed in the resurrection (8:11), but in the present rebellious and corruptible state of humankind, within which sin had made its dwelling (7:18, 20, 23, 25). (Wright, "Romans," 577)
I think this is the right track. The flesh, rather than Torah itself, was the cause of weakness. But of course, this creates some tension with the actual grammar of the passage itself. Paul does indeed say that Torah's weakness came "through/by the flesh" [διὰ τῆς σαρκός; dia tēs sarkos], but nevertheless it looks like Torah itself "was weakened." And this idea, as Jewett noted, is unique among the Pauline corpus and even the NT itself. And I still cannot escape the suspicious that, v. 3 notwithstanding, the rest of Romans 7.7–8.11 does not portray a weakened Torah.
I'm still not sure we've understood this verse rightly. Any suggestions?