Why will photosynthesis fail in 600 million years?

In a previous post about the future of life on Earth, I wrote about the presumed failure of photosynthesis in around 600 million years. Here’s why!
As our Sun ages, it increases in luminosity. As we all know, most plants rely on CO2 in order to function. Our planet has small amounts of CO2 in the atmosphere (0.041% by volume) and large amounts of carbon dioxide stored in it’s rocky crust. Scientists discovered that the increase in warmth due to luminosity also increases the amount of CO2 stored in silicate rocks. As the Sun’s luminosity will gradually increase, so will silicate rocks increase their capacity in storing carbon dioxide in our planet’s crust, leaving no CO2 in the atmosphere for plants to continue the photosynthesis process. As a result: no CO2 in the atmosphere equals no more photosynthesis!
This event expands on a timescale of 500 million years, so it will evolve very slowly. 
After the global failure of photosynthesis it might still be possible for cyanobacteria in Earth’s oceans to produce oxygen through photosynthesis. – Roman Alexander

(The question was originally asked by Stuart Graham)