A simple POD that could have resulted in an independent Burgundy surviving would have been if Mary the Rich had been born a male. Let’s say Philip IV is born in 1457 giving Charles the Bold an heir to continue his dynasty. The existence of a son could have possibly changed the way Charles pursued his goals. In OTL, Charles the Bold approached his plans with almost no regard as to how Mary would rule Burgundy after he was dead. Charles tried to do too much in one lifetime and wound up putting Burgundy in dire straits. But if he had a son, he could have afforded to be more patient in his plans to expand Burgundy.
Charles the Bold could have married his son to a daughter of Louis XI. In OTL, Louis XI betrothed his daughter Anne to Charles, with Champagne and Ponthieu as dowry. In this scenario, those counties could have been added to Burgundy. Even if Charles were killed in battle, the presence of an adult son trained to rule would have been able to prevent the disasters that occurred to Mary in OTL. Philip IV, assuming he is more patient than his father, could have negotiated a truce with Louis XI lasting until Louis’s death. If Louis still dies in 1483, then Philip IV can lead the French princes in a war against Charles VIII of France to reduce royal authority. In OTL, Louis XI made Anne the regent for Charles VIII, but in this scenario I doubt Louis would make the Duchess of Burgundy regent of France.
If Philip IV were able to use a civil war in France to force Charles VIII to release him from his feudal obligations, then Philip could focus his attention on the Holy Roman Empire. Philip could form an alliance with Archduke Maximilian that ensures that in return for money from Philip, Maximilian (upon becoming Emperor) will create a kingdom for Philip. This kingdom of Burgundy would still need to keep an eye on France in this scenario but (in alliance with England, the French princes, the Habsburgs, and possibly Castile/Aragon) would have the making of a formidable nation.