The time difference (synodic month) - (sidereal month) will not be constant. The reason for the variation is due to the eccentricity of the Moon's orbit: the Moon moves faster at perigee (closest to the Earth) than when at apogee (farthest from the Earth). If the Moon is near perigee around the time of New Moon, it takes less time for the Moon to "catch up" with the Sun, so the synodic month is shorter.
Also, the Moon's perigee and apogee distance changes from month to month due to the influence of the Sun. This also affects the speed of the Moon in its orbit. (The apparent speed of the Sun also changes because of the Earth's elliptical orbit around the Sun, but the variation is smaller.)
It may be helpful to take a "geocentric" view; that is, look at the motion of the Sun and Moon on the sky. In the following figure, a rare annular eclipse occurs with the Sun and Moon occulting the star Regulus ($\alpha$ Leonis). The days listed are the average sidereal and synodic periods. After 27.32 days (one sidereal month), the Moon is again aligned with Regulus. The Sun is farther east in the sky, so it takes a few more days for the Moon to catch up with the Sun and complete a synodic month (39.53 days).
Note: The distances travelled are approximate in this figure. The apparent size of the Sun and Moon are greatly exaggerated!
The two months are related by the speed of each object:
- average speed of Moon = 360 degrees/27.32 days
- average speed of Sun = 360 degrees/365.26 days
- distance travelled by the Moon in one synodic month = T*360/27.32
- distance travelled by the Sun in one synodic month = T*360/365.26
The two distances are not equal: the Moon moves an extra 360 degrees. So the length of the average synodic month, T, can be calculated by solving this equation:
It should be apparent from this equation that if the speed of the Moon varies, then the duration of the synodic month T will change as well.