Planets do not twinkle because:

i. Planets are very close to the earth.

ii. Hence, they cannot be seen as point sized sources.

iii. The light coming from the planets do not vary. Thus, causing no fluctuation in the position of planet.

iv. If we consider planets as a group of point-sized particle, then the light entering our eye from the individual source will become zero.

v. Causing no twinkling effect on the planet.

Hence, planets do not twinkle due to their small distance from the earth.

***note: when the object sometimes becomes brighter and sometimes fainter, this is the twinkling effect. It is caused by the fluctuation of the amount of light entering our eye from the object***