The planets seem to be quite large to us (because they are much nearer to the earth).
As a result, a planet can be thought of as a collection of a huge number of light point sources.
The dimming effect produced by point sources of light in one part of the planet is cancelled out by the brighter effect produced by point sources of light in the other part.
As a result, the brightness of a planet remains constant over time, and hence it does not appear to twinkle
Hence, The continuously changing atmosphere is unable to cause variations in the light coming from a big-sized planet (due to refraction) because of which the planet does not twinkle at all.