So long as there is ground above the water, that ground will be washed into the river and can replace mud that is washed away. This is called erosion. This would only stop if everything eroded to make the world completely flat, but this would be disrupted by plate tectonics.
An rivers get their water from the water cycle you learn about in elementary school. Water flows into the ocean, it evaporates, becomes clouds, the clouds rain on the land which then becomes the river.
Latest Answers