The recent edition of Luther's works (LW 59) gives the following footnote on page 288:
18 On justification by faith as "the article by which the Church stands or falls," see Commentary on the Psalms of Degrees (1532-33/1540), WA 40.3:351 (LW 66); cf. Commentary on Psalm 117 (1530), LW 14:37; Disptation for Palladius and Tilemann: On the Works of the Law and of Grace (1537), WA 39/1:205.2-5 (LW 60).1. The first reference can be found here, WA 40.3:351." "quia isto articulo stante stat Ecclesia, ruente ruit Ecclesia"—"Because if this article [of justification] stands, the church stands; if this article collapses, the church collapses" (ht: Justin Taylor for the translation). "LW 66" refers to a forthcoming English translation of this treatise.
2. "Commentary on Psalm 117 (1530), LW 14:37." This refers to volume 14 of Luther's Works in English. This page states,
My main reason for doing this is to move and instruct all who need it, to search out and deal with the core of our Christian doctrine, wherever it may be found throughout the Bible. And the core is this: that without any merit, as a gift of God’s pure grace in Christ, we attain righteousness, life, and salvation, and that there is no other way or path, no other means or effort, that can help us to attain it. Every day I experience only too well how insistently the devil assails this core in an effort to wipe it out. And although tired “saints” consider it unnecessary to keep at this matter—they imagine that they know it inside out and have learned all there is to know— still I know how wrong they are, and that they know absolutely nothing about the importance of this point. If this one teaching stands in its purity, then Christendom will also remain pure and good, undivided and unseparated; for this alone, and nothing else, makes and maintains Christendom. Everything else may be brilliantly counterfeited by false Christians and hypocrites; but where this falls, it is impossible to ward off any error or sectarian spirit. This I know indeed, and I have experienced it so often that without this teaching I could never refute what either the Turks or the Jews believe.3." Disptation for Palladius and Tilemann: On the Works of the Law and of Grace (1537), WA 39/1:205.2-5" can be found here. "(LW 60)" refers to a recent English edition of Luther's Works, but this appears to be an error. This treatise is not found in LW 60.
Karl Barth has an interesting overview of the saying here. He provides a good amount of references, but concludes: "The well-known description of the doctrine as the articulus stantis et cadentis ecclesiae does not seem to derive from Luther himself, but it is an exact statement of his view."