To my consideration, the answer lies within the terms. While the Russian and French revolutions were, basically internal affairs, as they wanted to overthrow the government held by actual Russians and French people respectively, the American revolution was actually an independence, as the government that was sought to be overthrown was English. As the source of the problem leaves the country, problems aren't as prone to reappear.
Speaking broadly the reason many revolutions have failed is because a victorious and popular General uses his popularity, particularly within the military, to consolidate power before the post-revolution State can be brought fully into existence. One of the reasons Trotsky - a charismatic leader, formidable rhetorician, and leader of the red army - was exiled and feared was because the Bolsheviks feared he'd become another Napoleon. So perhaps the principle reason is that George Washington didn't go mad with power and use his popularity become a military dictator.
I'm going to offer an alternate theory to /u/DaMadApe: The American Revolution faced no external threat, as did the French and Russian revolutions. In 1783, following the Peace of Paris, the United States had no immediate external enemies. It did not face the threat of invasion, and thus the government was able to focus on internal problems first and foremost. Thanks to this "breathing room," for lack of a better term, early Americans were allowed the time to settle internal conflicts caused by the Articles of Confederation and the formation of a new government. With external peace, the new United States was able to draft a constitution outlining a new government without interference.
Both France and Russia faced invasion immediately after the establishment of the revolutionary government. Once the revolutionary governments overthrew the existing order, they faced external problems. In 1792, following the end of the French constitutional assembly, France faced invasion on several fronts. It also faced problems with internal problems — counterrevoluntaries on one end of the scale and radical revolutionaries on the other end of the scale.
The United States faced these internal problems as well — think the Whiskey Rebellion for one example — but it was able to focus intellectual and physical resources on these internal problems where the French Revolution was distracted in multiple directions. The invasion of France by the First Coalition dissolved what support remained for the monarchy, and the constitutional monarchy collapsed. This permitted the Reign of Terror and all that came afterward. Had the constitutional monarchy been given time to stabilize, it could have lived on, just as the young American government was given time to draft a stronger document and structure that fixed the problems of the Articles of Confederation.
Now, look at Russia. Its circumstances were even more critical than that of France -- it was already invaded by the German army at the time of the February Revolution, which installed a moderate provisional government. The continued attacks of the German army fatally weakened the provisional government. One of the promises that government had made was that it would not send more troops to the front lines. When it did so, support for it began to decline.
After the October Revolution and the cease-fire with Germany, Russia was invaded again — this time by the Allies and Japan. As in the latter part of the French Revolution, drastic and bloody measures were taken by the revolutionary government to secure its rear area in order to successfully fight the war against the external enemy.
I think geography plays a role as well. The months it took for new British troops to arrive from England (and the challenges with communicating back and forth) severely limited to Britain's ability to respond to the colonist's efforts.
Essentially similar to the "internal" discussion above.
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