Why do people who flee while a trial is ongoing lose their right to appeal?
For example, during the trial of Andrew Luster, who fled the country during his trial: “The California Court of Appeal refused the appeal his attorneys filed on his behalf, [2] ruling that as a fugitive from justice, Luster had forfeited his right to appeal.”
He committed terrible crimes and deserves all the punishment he received but from a completely legal point of view, where is the precedent that someone who flees loses their constitutional right to an appeal?
Answers below in Comments Section

People who flee don’t lose their right to appeal.
“refused the appeal his attorneys filed on his behalf”
His attorneys appealed without his consent and he refused it. He wasn’t denied it.
First, there is no constitutional right to appeal. The right is purely statutory. (See Powers v. City of Richmond (1995) 10 Cal.4th 85.) If it was a constitutional right, Ruster might have been decided differently. (Note that Ruster did not “refuse his appeal,” it was the Court of Appeal which refused to hear the matter.)
The concept comes from a case called People v. Buffalo (1975) 49 Cal.App.3d 838, in which case the defendant escaped from custody while his appeal was pending. The Court of Appeal held that it had no jurisdiction over somebody who was no longer subject to the court’s process, and thus the appeal could be dismissed.
I think this rule is IMPROPERLY applied in cases such as Ruster. Ruster failed to appear DURING trial, and it was therefore proper to proceed with the trial in his absence–his flight was certainly a waiver of his right to be present at trial. However, since he did not know he was convicted, and had no notice of a sentencing date, it was IMPROPER for the court to impose judgment in his absence. (People v. Shelby (1980) 108 Cal.App.3d Supp. 7.) The court should have awaited his re-arrest, and then imposed a judgment from which he could have appealed.
It seems to me to be the height of sophistry to assert that while it is improper to sentence a defendant who fails to appear during trial in his absence, the defendant, by that same absence, loses the right to complain about that illegal order. In other words, I think Ruster was denied due process and that the reviewing court’s decision is manifestly in error.