ANSWER: The verses in Revelation that lack a reference to this tribe of Israel are found in chapter seven verses four to eight. Dan is the oldest son of Jacob (later renamed Israel) and Bilhah. His tribe was one of Israel's largest and most important groups.
After the Israelites left Egyptian bondage, a census showed Dan could field an army of 62,700 fighting men (Numbers 1:39). Only Judah had more men.
The quick answer to your question is that the Bible does not clearly tell us exactly why the tribe of Dan is omitted from the prophetic listing found in Revelation. They are certainly found in other lists that delineate the people of Israel (Numbers 2, 26, Joshua 19, and so on).
Scripture, however, does give us a few clues as to why God might have decided not to list Dan as part of the 144,000 Israelites saved during the Great Tribulation.
Because the tribes, minus Dan, are enumerated so specifically in Revelation 7, it is hard to accept the notion that the list in question 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 Israelite descendants will play in the End Time.
Although we may not know who would be part of each tribe that ultimately composes the 144,000 (or they may not know until it happens), God would. They would be, at least, part of the true Christians who stayed loyal to the Eternal and did not serve Babylon the Great.
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. Their worship of idols began right after they fought for and secured their inheritance in the Promised Land (Judges 18:1 - 2, 29 - 31). They became the first Israelites to commit this type of grievous sin.
The idolatry of Dan 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 he became afraid his new subjects would travel to Jerusalem, repent of splitting the kingdom, then kill him. His solution was to set up false gods within the kingdom that people could worship.
The first idol King Jeroboam placed was in the city of Dan (1Kings 12:26 - 29). The Danites continued to indulge in idols up to the time of their captivity in 723 B.C.
Another possible contributing factor as to why the tribe was omitted in the last book of Scripture is that they were slack about dealing with the pagan Canaanites in their midst. Dan also did not always participate with the rest of Israel in either defending the country or in attempts to seize more land.
When the prophetess Deborah sang about her victory over Jabin, the pagan Canaanite king, she openly asked why they stayed on their ships (Judges 5:17). As a balance, it has to be admitted that Asher was also slack in the battle song of Deborah.
Gilead stayed beyond Jordan. And why did Dan remain in ships? Asher continued on the seashore and remained in his havens (Judges 5:17, HBFV).
As a sidelight, the most well known Old Testament 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. We might never know for sure why this tribe is not in Revelation until we get a chance to ask Christ upon his return.