Why did Edmund Burke believe the French Revolution was doomed to fail?

Edmund Burke believed the French Revolution was doomed to failure because the French would not know how to properly use the liberty they had suddenly achieved for themselves. Unlike other thinkers of the time (notably Thomas Paine), Burke did not believe conceptualizing unfettered liberty as a natural right was a good thing, and he was a critic of what we might call the Radical Enlightenment.
Burke's understanding of liberty is best summarized by a passage from a letter he wrote to a Frenchman named Depont in 1789:

Permit me then to continue our conversation, and to tell you what the freedom is that I love, and that to which I think all men entitled. This is the more necessary, because, of all the loose terms in the world, liberty is the most indefinite. It is not solitary, unconnected, individual, selfish liberty, as if every man was to regulate the whole of his conduct by his own will. The liberty I mean is social freedom. It is that state of things in which liberty is secured by the equality of restraint. A constitution of things in which the liberty of no one man, and no body of men, and no number of men, can find means to trespass on the liberty of any person, or any description of persons, in the society. This kind of liberty is, indeed, but another name for justice; ascertained by wise laws, and secured by well-constructed institutions.

Burke believed the ability to use liberty properly was something that had to be learned. In Reflections on the Revolution in France, he argues that liberty is an "entailed inheritance" and famously describes a social contract "between those who are living, those who are dead, and those who are to be born." Throughout the text, he argues that the British have spent generations--going all the way back to the Magna Carta (1215)--protecting and generally improving their conception of liberty.
On the other hand, the French, who had long been under the rule of an absolute monarch, did not have a tradition of liberty to pass down. Burke believed that, without knowledge of how to be free, sudden liberation could be dangerous. (In making this argument, Burke is drawing upon Locke's famous distinction between "liberty" and "license" from the Two Treatises on Government.) He believed France would be susceptible to all the vices of populism. In one of the closing passages of the Reflections, he writes:

But when the leaders choose to make themselves bidders at an auction of popularity, their talents, in the construction of the state, will be of no service. They will become flatterers instead of legislators, the instruments, not the guides, of the people. If any of them should happen to propose a scheme of liberty, soberly limited and defined with proper qualifications, he will be immediately outbid by his competitors who will produce something more splendidly popular. Suspicions will be raised of his fidelity to his cause. Moderation will be stigmatized as the virtue of cowards, and compromise as the prudence of traitors, until, in hopes of preserving the credit which may enable him to temper and moderate, on some occasions, the popular leader is obliged to become active in propagating doctrines and establishing powers that will afterwards defeat any sober purpose at which he ultimately might have aimed.

Burke has been seen by his supporters as a bit of a prophet. The Reflections were written in 1790, and the Terror, a violent period of purges, occurred from 1793–4. He also wrote of the dangers of a military general taking power:

In the weakness of one kind of authority, and in the fluctuation of all, the officers of an army will remain for some time mutinous and full of faction until some popular general, who understands the art of conciliating the soldiery, and who possesses the true spirit of command, shall draw the eyes of all men upon himself. Armies will obey him on his personal account. There is no other way of securing military obedience in this state of things. But the moment in which that event shall happen, the person who really commands the army is your master — the master (that is little) of your king, the master of your Assembly, the master of your whole republic.

Napoléon Bonaparte took power in France two years after Burke's death.
https://oll.libertyfund.org/quotes/473