Discussion of secession in the United States is usually tainted by the connection with the term to the Civil War and slavery. This can be quite frustrating, as questions of secession are fundamental to the legitimacy of a government, and the topic can get derailed into talk about the evils of slavery, and how to solve them without war.
I think of the question of secession as being linked with the idea of the consent of the governed. How are they connected? The consent of the governed is the idea that a legitimate government is only legitimate if it has the consent of the people over which the it is ruling. This is fairly well accepted, and is a phrase used in both the Declaration of Independence, and a similar idea is expressed in the UN Universal Declaration of Human Rights: "The will of the people shall be the basis of the authority of government." Secession is what happens when a substantial subset of people withdraw their consent to be governed by a particular government, and separate from it.
For the governed people to meaningfully give consent, it must be possible for that consent to be withdrawn. If consent cannot be withdrawn, then a government that turns tyrannical is just as legitimate and consensual as a democratically elected government. So what should happen when a group ceases to consent to the current government? Under democratic ideals, they would vote in a new set of rulers to whom they consent. Now suppose that there is a significant geographic split, and the people in one region want to be ruled one way, and people in another region want to be ruled another way? Should the minority in that case be ruled by the majority from the other region? Or can the minority region autonomously withdraw consent to be ruled by the other region?
I think that the answer is fairly straightforward in the abstract. The people in the minority of the whole country should be allowed to split off from the nation, and choose their own form of government that has the consent of the people who live there, even though that was the minority of the people in the original nation as a whole. Furthermore, the independence of the minority region should not be dependent on the opinions of the majority region. If the minority region wishes independence, then any action by the majority region to stop the secession is seeking to deny the will of the people in that region. It could be viewed as a form of Imperialism.
So what happens if we continue this process? If there is another significant minority in the original minority (now majority) of this new country? Well, I think the same logic applies, and that region should be allowed to break off from the new country to form another country which has the consent of the governed.
Another side to think about consent of the governed is this: What should happen when an individual withdraws consent to be governed by the current regime? They could certainly be the majority of the people that occupy their property (assuming a land owner), so should they be able to withdraw consent unilaterally? If not, then how large a group do you need to revoke the consent? A city? A town? A county? A state? At what level do we draw the line?
I personally think that an individual can withdraw their consent to be governed, and they should be free to do so. The only valid retaliation would not be for the withdrawal of consent, but for aggressive action on the part of the individual. A state, company, or coalition certainly has the right to use the powers of defense delegated to them by the consenting members of that state, company, or coalition.
