Why did James Madison argue that separation of powers and checks and balances were particularly necessary in a republic?
James Madison believed that though people wanted to do good they would do evil unless checked and held accountable
The Articles of Confederation were based on the philosophy of Rousseau. The ideas was that people were basically good and that in a perfect environment with a minimum of government people would always do what was best for the community.
The Articles of Confederation did not work out very well.
The Constitution was based on the philosophy of Baron de Montiquese. In short this philosophy says that power corrupts and absolute power corrupts absolutely. The only way to preserve liberty and freedom is to limit the amount of power any one person or group of people can have.
The Constitution has work fairly well. The Congress can block the actions of the President and override the President's veto. The Supreme Court can declare the actions of both the President and Congress unconstitutional.
Recently both the President and the Supreme Court has superseded some of the powers of the Congress causing the balance of powers to become unbalanced.