To begin with, Charlemagne's Empire was continuation of a Franconian polity that already existed prior to the Fall of the Western Roman Empire, and was able to expand fairly rapidly following Roman decline. The Merovingians controlled a territory that contained much of what would become West Francia by the early 6th century CE. (Wikipedia's cleaned up version of Historical Atlas by William R. Shepherd, 1911)

As such, Franconian control over these territories was long-established, and relied less on the institutions Charlemagne had created to maintain control over the newly conquered territory. While Middle Francia (which included most of the Modern Netherlands and the Carolingian territories in Italy) did include a large amount of Austrasia, and even East Francia held some of it, West Francia had almost none of the territory that was added to Francia during Charlemagne's rule.

This allowed West Francia the luxury of long-established internal politics, laws and practices, which translates to stability and an easier time maintaining rule.

East Francia was further plagued by the reality that the Saxons in the Northern part of their territory were most definitely not Franks, and had only been converted to Christianity under Charlemagne's rule, by force. It's no coincidence that, although Christian, the first dynasty to successfully challenge Carolingian rule in East Francia was the Ottonian Dynasty, a Saxon dynasty that claimed descent from Widukind, a major leader of the pagan Saxons during the Saxon Wars of Charlemagne. (I'm afraid I don't have any reliable online sources for this, unless you consider Wikipedia reliable. In which case there's this: http://en.wikipedia.org/wiki/Widukind#Medieval)

Middle Francia, beyond having not nearly as many of the long-standing Francian lands as West Francia, had to contend with a wide variety of peoples within its borders. From the Frisians in the north to the Italians in the south. Furthermore, both West and East Francian rulers have had the desire for Middle Francian lands in their bids to claim all of Francia, and as such it has served as a site for frequent conflict.

All this forced what would become the rulers of the HRE, formed out of essentially Middle and East Francia, to delegate more power to local authorities than the West Francian kings had to. It is however important to recognize that medieval France was hardly a properly unified polity, and the HRE's emperorship was not always as weak as it ended up becoming after the Wars of Religion.

And it's important to take into account that the Wars of Religion did a great deal of damage to the power of the Holy Roman Emperor in the various vassal states. Not only did the rich and populous Netherlands secede, but the Emperor was forced to make many concessions to Lutheran and Calvinist rulers within the HRE.

However, it's worth remembering that for centuries, the Holy Roman Empire's borders were roughly analogous to the borders of Middle and East Francia, and that the Holy Roman Emperor was hardly a figurehead for most of the HRE's existence. Decentralized certainly, and between being an elected monarch and the occasional civil war for the Imperial Title, the Emperors were frequently forced to make concessions to keep (or obtain) the title, which prevented centralization and helped further decentralize the Empire.

tl;dr: West Francia was far more united to begin with, and it's not as much a tale of failure to stay united as much as inability to centralize power leading to local powers maintaining a higher degree of power and autonomy.

(Sorry for being unable to provide proper sourcing, I'm away from my work computer and my library for the time being. I hope this is useful regardless.)