The Jewish canon was still in a state of flux when the New Testament was being written. Therefore, early Christian authors drew freely from a wide variety of works, some of which were excluded from both the Jewish and Christian scriptures at a later date. 1st Enoch falls into that category.
The early church probably held theological views most similar to the Pharisee sect of Judaism. That meant that they would have accepted a larger selection of books than just the Torah (Genesis, Exodus, Leviticus, Numbers, and Deuteronomy), but not the full range of texts that have been found in the Qumran library. Enoch was not found in the 132 BCE translation of the Hebrew Bible into Greek (the Septuagint). Most likely, the text was not in it's final form at that time. However, many church fathers quoted Enoch, so it must have been translated into Greek by the first and second century CE. Only a few fragments of Greek copies remain.
It's clear that the author of Jude directly quoted Enoch 1:9 and properly attributed the quotation:
It was also about these that Enoch, the seventh from Adam, prophesied, saying, “Behold, the Lord comes with ten thousands of his holy ones, to execute judgment on all and to convict all the ungodly of all their deeds of ungodliness that they have committed in such an ungodly way, and of all the harsh things that ungodly sinners have spoken against him.”—Jude 1:14-15 (ESV)
Whether he had a Greek translation available or translated it directly from Aramaic (or some other language) is unknown. There are textual variations, but we can be pretty confident that this quotation comes from Enoch and not Deuteronomy 33:2.
Tertullian directly addresses the issue:
But since Enoch in the same Scripture has preached likewise concerning the Lord, nothing at all must be rejected by us which pertains to us; and we read that “every Scripture suitable for edification is divinely inspired.” By the Jews it may now seem to have been rejected for that (very) reason, just like all the other (portions) nearly which tell of Christ. Nor, of course, is this fact wonderful, that they did not receive some Scriptures which spake of Him whom even in person, speaking in their presence, they were not to receive. To these considerations is added the fact that Enoch possesses a testimony in the Apostle Jude.
His argument uses an ingenious interpretation of 2nd Timothy to show that Enoch was inspired because it contains prophecies about Jesus. He also argues that it was rejected by the Jews for that same reason. That Jude quoted a portion is merely secondary evidence.
Given this promising start, why didn't the church accept Enoch? Ultimately, I think the answer lies in the difficulty the church had in deciding on the Christian texts to be included. Even at the time of Eusebius the question of which texts belonged in the New Testament was disputed. 2nd Peter, for instance, was considered doubtful. The Old Testament was a less pressing matter and it seems that the church generally accepted the Jewish Scripture. Eusebius quotes Origen:
It should be stated that the canonical books, as the Hebrews have handed them down, are twenty-two; corresponding with the number of their letters.
Of course, the numbers don't quite add up. Even the smallest reckoning is 24 books. But the point is that Christians began to accept the Jewish canon as authoritative. That meant ignoring books like Enoch that weren't broadly accepted by 1st and 2nd century Jews.
Before Jerome, most Christians simply used the Septuagint (or Latin translations of it) because it was convenient, it was quoted (and therefore used) by the apostles, and some (such as Augustine) considered the translation itself inspired. Obviously, Enoch was not found in that collection. After Jerome, the Latin church shifted to using the Vulgate, which also didn't include Enoch. So for the vast majority of Christian traditions Enoch simply fell out of use.
It should be noted that at 108 chapters and about the same number of pages in a modern edition, Enoch is a relatively long book to be copied and translated. Before Gutenberg, a text really needed to justify its value in order to be propagated. While the text contains much detail that isn't found elsewhere in the Hebrew Bible, the material is fairly esoteric and not terribly applicable for the early church (unlike Revelation). The formation of the canon (from a historical viewpoint) was a chaotic process.
There's a ton of interesting things in Enoch and other non-canonical works, but as a Christian, I don't feel like we are missing out on much by not reading them. God has used the Church, with all of her missteps and human failings, to produce a canon that fully describes His character and plan for the world.