I think you are asking about 2 different things:
#1 Someone who has been sentenced to death
As mentioned above the appellate process is LENGTHY (state court of appeals, state supreme court, us supreme court). Moreover, its not just 1 appeal many death row inmates are on their multiple appeal attempts so you have to rinse/repeat the entire process.
You might ask how can they appeal the same trial multiple times? Well they simply claim that new evidence has come to light. Of course, the problem they run into legally is the legal standard is new evidence has come to light and it was not discoverable at the time of trial. (Think DNA evidence for convicts convicted before DNA technology became available).
Recently, states are having problems obtaining the necessary mix of drugs for lethal injections. Your firing squad idea would likely be ruled "cruel and unusual punishment" in violation of the Constitution. Now why that would be considered "cruel and unusual" when we hung people at the time the Constitution was written and adopted is laughable to anyone that uses logic/reasoning. But the left reads into the Constitution what it sees fit and ignores what it doesn't like. (see e.g., 2nd Amendment)
Anti-death penalty advocates have been pretty successful in recent years going after the companies that make the drugs that are used in lethal injections by picketing their company locations, etc... This has caused somewhat of a shortage of the drug "cocktail" that is used for lethal injection.
#2 Someone with a sentence so.... long they will never leave prison alive.
The answer of why we don't execute them is simple they were not sentenced by a jury of their peers (or judge if they waived their right to a jury trial) to die. That would unquestionably be Unconstitutional to execute someone who has not been sentenced to execution.
Of course, you do have a point of why do some people get sentenced to several hundred year sentences instead of just a sentence of life without the possibility of parole. Usually that is because of the way that statutes are written in the states that for whatever reason will permit a 1000 year sentence for multiple counts of X crime but would not permit a sentence of life without the possibility of parole.
Bookmarks