The reasons for the success of the Patriots can be enumerated and explained in a relatively simple and straightforward manner, maybe surprisingly so for the complexity and importance of the event:
1) The British were divided on the proper way to stop the rebellion and even on the question of whether the Americans were justified in rebelling against the Crown. The Patriots regarded themselves as merely standing up for their rights as Englishmen. They believed they were entitled to the rights enshrined in the (English) Constitution and in the principles of the Whig Party to which they were faithful. Many of the British military commanders were actually somewhat in sympathy with the Americans and had no intention of prosecuting a "total war" against them, since the English on both sides of the Atlantic were regarded by many as essentially the same people. Despite the popular view of the war which has come down to us, much of it due to propaganda from the Patriot side, in many instances the British prosecuted the conflict weakly and did not take the rebellion seriously.
2) The British eventually found that they could take territory militarily, but unlike in the conventional wars fought on the European continent, this did not result in the surrender of the enemy or bring the war closer to a conclusion. As long as Washington kept his army intact, the war went on. When Howe took Philadelphia in 1777, it meant virtually nothing in the progress of the war. This was despite Philadelphia being the most important city in the Colonies. The conflict was spread out over too wide a territory for one battle to be important. The rebels had multiple armies that could spring into action at short notice, such as the force that defeated Burgoyne at Saratoga. Their victory at Saratoga essentially nullified Howe's victory in Pennsylvania, which was short-lived and meaningless anyway.
3) Individual battle victories, like the conquering of territory, were inconsequential in the long run. In the Southern campaign in 1780-81 Nathaniel Greene lost every battle he fought against the British, but still wore them down until Cornwallis had no viable option but to hole up in Yorktown and wait for relief, which never came because the French fleet arrived first and blockaded the British on one side, with Washington's and Rochambeau's armies on the other.
4) The entry of France on the Patriot side in 1778 probably tipped the balance and nullified whatever chances ever existed for a British victory. The American Revolution had now become another in Europe's endless series of international conflicts. The protection of their possessions in the West Indies, with their valuable commodities, now became of more significance to the British than winning the war on the American mainland. In 1781, after six and a half years of endless expenditures and no progress, culminating in defeat at Yorktown, Parliament realized the war was useless. The Whig opposition came into power, and the decision was made to recognize the independence of the Colonies, now the United States.