All representative Republics in the past have degenerated toward democracy, and then failed.
Possibly. Care to provide examples? Especially if you're going to use words like "all."
I would contend that a lot of representative democracies have failed, but a lot of them not from an excess of democracy. Often quite the opposite, with oligarchies or aristocracies gradually acquiring more power.
It also should be pointed out that there were no representative Republics in the ancient world. The novel idea of electing representatives to govern grew out of the middle ages.