ANSWER: The quick and easy answer to your question is that the Bible does not clearly tell us exactly why the tribe is omitted from the prophetic listing found in Revelation the seventh chapter. Dan is certainly found in other lists that delineate the people of Israel (Numbers 2, 26; Joshua 19, etc.). The Bible does, however, give us clues as to why God might have decided not to list them.
Because the tribes are enumerated so specifically in Revelation 7, it's hard to accept the notion it refers to people who are merely spiritual Israel (the church in general). Instead, it makes sense it refers to Christians given special protection or a special role the descendants of the Israelites play in the End Time. We may not know now who would be part of each tribe that ultimately composes the 144,000 (or they may not know until it happens), but God would. They would be at least part of the true Christians who stayed loyal to God and didn't serve Babylon the Great or her daughter harlots, or indulged in idolatry like Dan.
One quite common speculation as to why the tribe of Dan is not listed in Revelation comes from the fact that they had an enormous difficulty with idolatry. They, early in their history, became devoted to such practices (in fact, the first Israelites to do so) and continued them up to the time of their captivity in 723 B.C. Its worship of idols began right after they fought for and secured their inheritance in the promised land (Judges 18:1 - 2, 29 - 31).
Later in its history, Dan's idolatry was further encouraged when they, along with nine other tribes, split from a united Israel after the death of Solomon. The newly formed Northern Kingdom was ruled by King Jeroboam. Right after he took power (in 930 B.C.) he became afraid his new subjects would travel to Jerusalem to worship God, repent of splitting from their brethren, put themselves back under the rule of Solomon' son and kill him. His solution was to set up false gods within the boundaries of his kingdom to keep the people separate from their brethren in Judah's Kingdom. The first idol was placed in the city of Dan (see 1Kings 12:26 - 29).
One theory sometimes discussed is that Dan is not listed because the Antichrist will be a Danite. There is no known credible Biblical proof, however, to back up this claim.
One likely contributing factor to the tribe of Dan's omission in Revelation is that they, who were located on the northern-most border of the area originally given by God to Israel, were slack about dealing with the Canaanites (who were pagans) in their midst.
Dan also did not always participate with the rest of the Israelite tribes in defending Israel or going on the offensive. When the prophetess Deborah sang about her victory over Jabin, the pagan Canaanite king, she openly asked WHY this set of Israelites stayed on their ships (Judges 5:17). As a balance, it has to be admitted that another tribe (Asher) was also slack in the battle Deborah sung about.
As a sidelight, the most well-known Biblical person from the tribe of Dan was Samson. Although he was a judge of Israel for twenty years and known for his miraculous strength, he was somewhat of a carnal man (not very spiritual) for a good part of his life. Ultimately, the real issue is not about people listed in Revelation but rather that those who believe in Scripture, when confronted with mysteries like this, still need to live their lives in a Godly fashion. May we strive to be there!