If we're looking at Philip the Good's efforts to create an independent kingdom from 1419 onwards, a good bet might be for Henry V of England live a few years longer to be crowned King of France. By this point I think an Anglo-French union is practically impossible in the long term but such an event will drag the HYW out and weaken Valois power for decades, giving Burgundy more breathing space.
After Henry V dies, Henry VI will struggle greatly to hold onto France but his legitimacy will make it all very messy. Also if anything like the War of the Roses takes place, English attention will be diverted and the HYW will probably be over by the 1460s/1470s however English Kings might be keener in the future to try and seize French lands in the future due to their brief reign there. All in all the French can't concentrate on Burgundy or the other Duchies like Brittany, plus butterflies will see King Louis XI of France, the "Spider-King" never born, assuming some one less Machievellian takes the French throne, all in all Burgundy has a far better chance of surviving.
Economically Burgundy's power was the Flemish ports and despite Dijon being the true capital, Philip held court much of his reign in Brussels. As such come any Reformation-esque event, I'd imagine them going Protestant, however ironically their homelands around Dijon might not leading to plenty of problems.
A major problem for Burgundy would be seizing the lands that seperated their own, they did seize Lorraine in OTL in the 1470s, under Charles the Bold's reign but this was one of his many rash action that led to his death and the fracturing of his lands.
Say Charles is less 'bold' or simply the French can't offer decent opposition due to the war with England and a lesser king (Charles wasn't a moron but Louis XI was a genius). I think sheer wealth would have eventually seen the Burgundians gain a crown at some in the early 1500s.
One interesting thing to consider is how much a lasting Burgundy will change European military history, the collapse of such a large web of duchies, lordships etc. in a strategically vital area was a massive motivator for wars into the 18th century as evenyone tried to seize the them, a unified strong Burgundy may lead to stability of a sort but it will also means there's another serious player in European politics, and certainly with the Flemish ports the Age of Discovery will see Burgundian ships sailing the world.
In the long run Europe may become pretty unrecognisable but given the widespread nature of the state in the 15th century I think you may end up with Burgundy effectively becoming a united Low Countries and there's still chance that even that will be fractured by language, religion and ethnicity, although who knows what social movements and government plands may take place to unite or divided the people's of the country.
I think such a state could last into the 20th century if we're conservative about butterflies (ie the general course of history is similar to ours), perhaps a great or middle power, the industrial revolution will certainly be happening there and with a united polity the Low Countries may be one of the few places alnogside England that has a chance of kick starting an Industrial Revolution.
By today though I'd hazard the various groups of Germans, French, Wallon and Flemish/Dutch might end up parting into their own states if they haven't amalgamated (not impossible in 500 years).