No bother. And, no customer on this site is a "client," because no attorney in this venue is practicing law. We're just exercising our respective 1st Amendment rights to free expression.
There is no "constitutional right" to an appeal. In state jurisdictions, a criminal defendant is generally guaranteed at least one appeal. In a civil action, all appeals are at the discretion of the appellate court.
For capital punishment cases, the judicial system will generally allow the appeal to go all the way to the highest court in the State, and usually to the U.S. Supreme Court, at least for consideration by one judge for an injunction.
There's a decent discussion of the issue at: http://faculty.ncwc.edu/mstevens/325/325lect09.htm (scroll down a few screens).
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Retired (mostly)