Communication != Contribution
There are a few considerations that factor in to the decision that the masters of an empire take when faced with a request for independence of a colonial state;
1) Ongoing Contributions of the Colony to the Empire
2) Ongoing Expenditure in maintaining / defending that colony
3) Reputational Damage
Let's deal with these one by one. A colony that is contributing to the empire in a critical way (either it is a contribution well above the cost of maintenance and defence, or it is a source of a critical resource that is not available elsewhere) is unlikely to get any traction on an attempt to assert independence. It's in the interest of the Empire to preserve the existing relationship.
A colony can solve this problem by either agreeing to generous trade arrangements, ensuring that there are alternative sources of critical resources that the Empire needs, or by finding their own access to these critical resources to be depleted. So, if there is a resource that the colony is obligated to provide but production is reduced due to 'critical shortages' or whatever excuse you can sell to the Empire, your usefulness reduces. It sounds counter-intuitive but if the Empire genuinely believes they have sucked you dry of what they need, they tend to lose interest, especially given the cost of maintaining you as a dependent colony.
That of course leads us to point 2 and the fact that it takes 100 years to get from the core to the outer colony tells me that shipping goods or troops there is going to be hideously expensive. If you can't provide them what they need, and it's going to cost them more to keep you in the empire either through concessions or through military action, they are less inclined to do so. A bad investment is a bad investment whether it is a flutter on a dodgy horse at the races or in maintaining and defending a non-performing colony. Good leaders would understand that so wouldn't press the issue if they were approached in a respectful way with their request.
That brings us into point number 3 - if we were to look at the American Declaration of Independence as an example, this is probably the classic example of what not to do on both sides.
Britain was unresponsive to the requests of the Americans and saw their colony as little more than a resource that needed to do as it was told.
America boldly declared themselves independent in a 'sod-you' to the British, who were forced to respond in an attempt to preserve their reputation on the international stage.
So; if your outer colony really wants independence, all it has to do is follow 3 simple steps;
1) Minimise your usefulness
2) Maximise your cost of maintenance (already done in part by the tyranny of distance)
3) Ask nicely
There are plenty of examples of how this works in practice. Just look at pretty much every African nation in the post-imperial era. Also look at India, Canada, and Australia as examples of how to detach from Britain with minimal, if any, bloodshed.
The mistake that can be made (and we learn this from the Roman experience) is to say that independence is a threat to an empire. That empires must by necessity grow. This just isn't the case and good leaders that have learnt from history know that and as such are not going to push the issue unless they're slapped in the face.
In short, gaining your independence may be a lot easier than you're led to think by those in power in the Empire. They're not going to advertise the fact but if a few colonies on the fringe want to leave they may actually breathe a sigh of relief; more resources to spread across the rest of their (now smaller) borders to protect themselves and their subjects.