You have the right to represent yourself, but not another person or entity, which is what you would be doing if you attempted to represent your limited liability entity in court. It doesn't matter if you're the sole shareholder or not, you and the company are not one and the same.
Except that such logic seems to vanish in small claims court (where I can represent my corporation), and before the USPTO Trademark Trial and Appeals Board (where I can represent my corporation)...which means that it's really not very logical at all.
The details of small claims courts vary wildly from state to state, but more importantly, they're not courts of general jurisdiction. They have severe restrictions on what they can and can't do, and the losing party is often entitled to a de novo trial in a court of general jurisdiction.
The USPTO appeals board you mentioned is not a court at all. It is an administrative body whose holdings are again subject to review in US District Court.
Small claims courts are not much different from arbitration. There are no consequences to not showing up or participating, as losing simply means that you can move the matter to a new (i.e., independent) case in a real courtroom with a real judge.
I cannot defend the USPTO; much of what they do is indefensible.
