They seem to have had a lot of advantages, including land that the French and Germans fought over for hundreds of years. Why didn't they succeed and how close did they get?
Well, what constitutes a "viable state" in your view? -- A modern nation state? It that's the case, the answer is easy: The Kingdom of Burgundy ceased to exist long before the rise of nationalism. If not, then you need to further explain what you mean by your question, I think.
See azods answer. But Burgundy never was restored because when Burgundian land was taken from the Confederation of thhe Rhine during the rise of the French Empire many of the lands belonging to the kingdom were taken by france and the rest being kept by a french owned Rhineland. With a cultural split such as that it can not be easy to restore an old kingdom, especiall when the split is owned by countries with power like france and soon to be Germany. No source cause im on my phone, but i read most of this while writing an essay on the fall and consequences of the HRE.
edit: yeah i repeated france and germany close to 4 times. idc.