Since the Didache was discovered in the late 19th century, scholars have provided a number of rationales, ranging from the typical standards of canonicity (late age, mysterious authorship, poor quality) to its association with an early heresy.

Age

The simplest explanation that many scholars have provided, either directly or indirectly, is that the work was not written in the apostolic age. Such arguments were more common in the years immediately following the discovery of the Didache; Charles Bigg argued for a fourth-century date,¹ while J. A. Robinson held that:

the writer of the Didache took the Two Ways from Barnabas, and also made use of the Shepherd of Hermas; and [...] consequently he cannot have written at an earlier date than between 140 and 160 A. D.²

The discovery of the Dead Sea Scrolls in 1948 led to most scholars to reject this idea of the Didache depending on Barnabas. But Bruce Metzger (1989) reports that "most" scholars still "prefer a date in the first half of the second century."³ That puts it on the very fringes of the apostolic age.

It's true that modern dating discussions do not necessarily tell us what the fathers thought about the age of the work, which makes this probably the weakest point. Furthermore, more recent scholars have trended toward earlier dates for the work, and have largely abandoned this explanation for the Didache's exclusion from the canon.

Authorship

Concerns about the authorship of the Didache are expressed in two ways: the author himself, and the location where he wrote.

Not surprisingly, the early scholars that argued for a late date (again, an idea that is now widely rejected) find no evidence for apostolic authorship. Robinson, for example, argues that the "mysterious" author simply recast the Epistle of Barnabas,⁴ and "was merely imaginatively reconstructing" what he thought was the teaching of the twelve apostles.⁵

Bruce Metzger interacts with the authority alleged in the title of the work:

The authority for these teachings, as suggested by the subtitle, is none other than Jesus through the mediation of the apostles. The word 'apostles', however, does not occur in the book itself, except at xi. 3–6 where it refers, not to the Twelve or Paul, but to itinerant evangelists. The title, therefore, seems to have been added sometime after the document was drawn up.⁶

Many scholars prefer a rural origin for the work, perhaps in a relatively "isolated" Christian community, like Syria.⁷ Aaron Milavec suggests that the consensus among scholars in the 19th century and earlier was that this was the reason the fathers rejected the Didache:

Everyone knew that Origen and Athanasius had made early reference to the Didache by way of naming ancient works whose reputation was too local to allow inclusion in the universal canon.⁸

This is still seen as the likely cause of its rejection by some today:

The Didache was not incorporated into the Canon (not for any heretical teaching that it contained, but probably simply because it had stayed too closely bound to its roots within Israel).⁹

Quality

The quality of the Didache is also sometimes cited as a rationale for rejecting the work. Henry Clay Vedder's analysis is typical:

Except that the first part is little more than a chain of quotations from the apostolic Scriptures, it is difficult to understand how any Father should have come to quote it as Scripture, as Clement of Alexandria undoubtedly did, since its quality is so different from the canonical writings. That difference of quality is enough to account for the fact that Clement stands quite solitary in his treatment of the Didache as having the character or authority of Scripture.¹⁰

As an aside, it's worth noting that many are much more hesitant to say that Clement quoted the Didache; another option given by those preferring a later date is that Clement was quoting a work that is now lost but served as a source for the author of the Didache.¹¹

Montanism

Perhaps the most intriguing rationale given for the Didache's rejection is its perceived support for Montanism, or New Prophecy. In the late second century, this movement, emphasizing new prophecies and the spontaneity of the Holy Spirit, led to significant conflict in the early church. Tertullian was a prominent proponent, but many adherents were excommunicated and the movement was ultimately regarded to be heretical.

In this theological milieu, the argument goes, a work referring to "prophets," like the Didache, could not have been accepted as canonical: the church fathers were reacting against a heretical movement and considered the Didache to be associated with it. Some scholars contend that as a second century work it was itself proto-Montanist,¹² but others, holding to an earlier date of composition, argue that its mere mention of prophecy in the church (11:3–11) was damning. Aaron Milavec makes the case:

Owing to the massive reaction against the New Prophecy, prophecy of any kind in the church became suspect during the third century. In this climate, the Didache itself may have become suspect in many circles because it had been used to sustain the claims of the New Prophecy. Interestingly enough, this was the very time when church councils were endeavoring to hammer out a universal canon of inspired books. In this climate, needless to say, the Didache did not make it into the canon. [...] Had the New Prophecy not erupted in North Africa and had the backlash against it not been so vigorous, then we would surely have been reading the Didache in our bound versions of the Christian Scriptures today.¹³

Summary

Scholars have suggested the traditional arguments against canonicity—late date, mysterious authorship, merely local influence, and low quality. But perhaps these traditional arguments were supplemented by concerns that the work, if not heretical itself, supported a heretical movement, and thus could not be accepted into the canon.

References and notes:

1. Bigg, The Doctrine of the Twelve Apostles, p23
2. Robinson, Barnabas, Hermas and the Didache, p45
3. Metzger, The Canon of the New Testament, p49–50
4. Robinson, p70
5. Draper, The Didache in Modern Research: 1996, p10
6. Metzger, p50
7. Early Christian Writings: Didache. See particularly the quotes from Crossan ("My own preference for a rural over an urban setting comes [...] from the Didache's rhetorical serenity, ungendered equality, and striking difference from so many other early Christian texts") and Kraft ("most commentators now seem to opt for Syria (Audet 1958; Hazelden Walker 1966; Rordorf and Tullier 1978) or Syro-Palestine (Niederwimmer 1977) as the place of origin").
8. Milavec, The Didache, p4
9. Patrick J. Hartin, "Ethics in the Letter of James, the Gospel of Matthew, and the Didache," in Matthew, James, and Didache, p314
10. Vedder, Our New Testament, p225
11. Robinson, p62
12. Draper, p11–12, mentioning Connolly and Kraft.
13. Milavec, p489