The Loyalists either fled the country- especially if they'd been part of Loyalist troops fighting against the Continental Army- or sheltered in place: they were in no position to try to continue the conflict.

However, there was a very strong imbalance in political power that had existed before the War between the western frontier and the east coast. In North Carolina especially, the state government had been completely controlled by the wealthy lowland planters, who ran it for their benefit. Before the war, frustrations in the west over corrupt appointed officials and exorbitant fees had grown to the point of revolt. The rebels- the Regulators- were brutally suppressed by the royal governor. As a result, when the eastern government decided to join with the Patriots in the War, many of the westerners remained Loyalist...at least initially.

After the War tensions still remained. The Boston merchants of Massachusetts were desperate to resume trade, but with the massive international War debt, credit abroad was impossible to find. The MA legislature, controlled by the eastern merchants, passed a law in 1786 requiring all taxes to be paid in hard currency. This was an enormous hardship- hard currency was in very short supply- and it was especially hard on the farmers of western MA, who had been doing business with personal notes and carrying debts and credits in their books ( essentially like trading IOU's) . Non-payment of taxes would result in their properties being sold at auction, and there was a revolt, led by a man named Daniel Shays. After a show of arms it was dispersed, most of the rebels pardoned, the law rescinded and the authors of the law failed to be re-elected. But the need to raise money to erase the War debt remained. After the creation of the Federal government, in 1791 one of Alexander Hamilton's ideas for this was a tax on whiskey. It was badly written, taxing small producers by the gallon and big producers with a yearly fee that was lower ( most of the producers in the west were small) and requiring it to be paid in hard currency- which , like before in western Massachusetts, was in short supply in the west. Whiskey was cheaper in the west, so in effect, then, the tax was higher on the frontier. And on the frontier, whiskey was a very important trade item, really an alternate currency.

Worse, although the end of the War had allowed a flood of settlers to pour into previously off-limit western territories, the Native nations had not been a party to the peace treaty. Frontier settlements were often attacked and settlers killed, and the settlers would as often retaliate. Two ill-conceived campaigns to conquer the territory and the Native nations in 1790 and 1791 resulted in defeats for the US, and as a result the frontier population felt very much left to its own defenses, abandoned by the east. The new whiskey tax was the last insult, and a revolt broke out in western Pennsylvania at Redstone, now Brownsville. The Pennsylvania revolt was put down, with George Washington himself in command. But the Whiskey Rebellion had very wide support all along the frontier. Not until some of the western Native nations were defeated, at the Battle of Fallen Timbers, and the new western states of Tennessee, Kentucky and Ohio created, did the tensions between east and west begin to subside.

Slaughter, T. P. (1988). The Whiskey Rebellion: Frontier Epilogue to the American Revolution (Reprint ed.). Oxford University Press.