How does a stalagmite form? 

The question addresses several points: Chemical equilibrium: The CO2 in the solution (drip water) and in the cave air are initially not in chemical equilibrium. This is because the drip water is enriched with the CO2 from the soil (where we typically find very high CO2 concentrations) while cave air has lower CO2 concentrations. Solubility of CaCO3: Some minerals dissolve in pure water. This is not the case for CaCO3, which can be considered as nearly insoluble in water. With CO2 dissolving in (and acidifying) the water, the solubility of CaCO3 in water increases. Evaporation as driver for carbonate precipitation: Humidity in caves is typically around 100%, so evaporation will not occur. Even if (for whatever reasons) only the CO2-independent solubility played a role, there will typically be no reason, why the CaCO3 would precipitate (if there is no change in temperature, which mostly is true for natural cave systems).