Precession refers to the slowly changing position of the equinox resulting from variations in the orientation of Earth's axis in space. Precession, and variations in the rate of precession, does not affect the absolute rotation period of the Earth on its axis and the mean solar day.

According to the findings of the Binary Research Institute, compelling scientific data exists that shows an increase in the calculated precession rates over the last 100 years.

http://www.binaryresearchinstitute.org/calculations/precession.shtml

Astronomers argue that such data merely reflects an improvement in the measurement due to technological advances. But Newcomb's ingenious observations, which resulted in the precise determination of the tropical year, should not be underestimated. It was a major accomplishment in the field of astronomy, equaled perhaps only by the observations of William Markowitz about four decades later. Measuring the transits and the occultation period of the stars by the moon, Markowitz was able to determine the tropical year precisely to one hundred thousands of a second, using quartz clocks.

Nowadays, cesium atomic clocks are the most accurate clocks available for time measurements. With a deviation of only one second in about two million years, atomic clocks provide us with a highly uniform measure of time due to the extremely stable oscillation of the Cesium atoms. Although the atomic second can be considered as absolutely constant, it is about 3 × 10E-8 s shorter in duration than the SI second. Therefore, every now and then so-called leap seconds have to be inserted. While the uniform time scale of the atomic clock allows us to precisely measure sidereal time, atomic time needs to be synchronized to the fundamental time interval of Earth's tropical-sidereal year of 31,556,925.97474 seconds.

So by using various non-specified sidereal frames of reference, which are considered fixed in relation to the moving and imaginary equinoctial point in the sky, astronomers were able to repeatedly derive the exact length of the tropical year despite apparent inaccuracies in the measurements of precession. In other words, the length of the tropical or equinoctial year remains unchanged, whereas the length of the sidereal year depends (according to the International Astronomical Union) upon the adopted value of the precession.

Still - astronomers claim that the equinoctial or tropical year is not the 360-degree orbit period of our Earth around the Sun, but about 50.26" less or roughly 20 minutes shorter than a sidereal year. Fortunately, the astronomical data on the solar eclipse cycle shows with mathematical exactitude that the equinoctial year is, in fact, Earth's actual 360-degree orbit period around the sun.

Dr. Myles Standish, an expert at JPL, had this to say about precession and sidereal time measurement:

"[...] Precession defined, formulated, and calculated using the basic laws of physics, found to be consistent with observations. Precession has now been measured accurate to the 99.999% level. [...] ... the numerical value [for a sidereal year of 365.25636042094 mean solar days] comes from Newcomb's "Theory of the Sun", used for his (1898) "Tables of the Motion of the Earth on its Axis and Around the Sun". [...] The difference in the two rates is 5024"93/cty; obviously, precession, even though the value of 5025.64 has long been known as "Newcomb's precession". [...] The modern value is 5026"47/tropical century (5029"0966 per Julian century), accurate to 1 or 2 units in the last figure given. Newcomb's Theory is cast in the precessing, of-date frame. [...] ... it was the frame most naturally observed (mainly, transits). [...] In order to find inertial space, one must remove the precession, a quantity that could not be determined as accurately or as easily back then - it involved detailed analysis of star motions and the removal of galactic rotation, star-streaming, etc. Nowadays, we have accurate VLBI measurements with respect to the (inertial) quasars, so the determination of the earth's orientation is anchored to inertial space (the ICRF - International Celestial Reference Frame), and precession is measured directly. Over a couple of decades, now, precession is known to a couple of hundredths of an arcsecond per century. [...] There is no real relevance of the sidereal YEAR to modern astronomy. [...] The quoted value, as shown above, comes from Newcomb's Theory, is referred to inertial space; it is evident that he applied precession to the tropical year in order to derive it. Therefore, it refers to motion in inertial space. [...] When a more modern value for precession was adopted in 1976, this ratio changed slightly. However, the basic method is unaltered. In practice, since the rotation of the earth is not completely predictable, the rotation of the earth gets measured on a daily basis, and the results of the measurements get applied in order to get the most accurate earth orientation possible."

The data on the mean transit period of Sirius (an inertial frame of reference) shows that over larger time frames the measurement does not reflect precession. According to Dr. Standish, the measurements were sufficiently accurate, but not the interpretation:

As any expert of scientific reasoning will undoubtedly agree, the data should speak for itself.