There were at least two problems after the Revolutionary War that were related to democracy. One was the weakness of the federal government and the other was the demand for populist laws in many states. Both of these caused enough problems that people decided to write a new constitution to replace the Articles of Confederation.
The Articles of Confederation made the national government too weak because of democracy. The people of the new United States wanted the national government to be weak because they did not want it to take away their rights the way (they felt) that the British government had. Therefore, they created the Articles of Confederation, which made the states very powerful and the national government very weak. This was a problem because there were many things (including imposing taxes, maintaining an army, and preventing trade wars between the states) that the national government could not do.
The other problem was the demand for populist laws that would be passed by states. The voters in the states were mainly relatively poor farmers. They wanted laws that would help them financially. Some states passed laws, for example, forgiving debts. This helped poor farmers, but it hurt the rich who had lent them the money. In other states, like Massachusetts, the government resisted passing these populist laws. In that state, the government’s resistance led to a populist rebellion now known as Shays’ Rebellion. These laws, and anger by people when those laws were not passed, were seen as a problem that was caused by democracy. Both of these problems led to the creation of the United States Constitution.