http://www.jpl.nasa.gov/news/news.php?feature=4643&utm_source=iContact&utm_medium=email&utm_campaign=NASAJPL&utm_content=weekly20150702-4
https://en.wikipedia.org/wiki/Leap_second
You ask 'geocentrists' to explain what? In a geocentric scenario it is the rotation of the universe that brings about the time of a day. So if a day slows it is the universe that is slowing. God must be getting tired.
Your website says: The average length of a day, based on how long it takes Earth to rotate - is about 86,400.002 seconds long.
Scientists estimate that the mean solar day hasn't been 86,400 seconds long since the year 1820 or so.
'Estimate?' Have they a record of this? Is there a record of an 1820 timing of 86,400.000 seconds I wonder. Bet there isn't
Tell you what. If they come back in 100 years and show an earth day is 86,400.003 seconds long, then they will have proved the day is getting slower.
One other word of advice. I myself am a biblical geocentrist. I take the advice of St Thomas Aquinas
‘The knowledge proper to this science of theology comes through divine revelation and not through natural reason. Therefore, it has no concern to prove principles of other sciences, but only to judge them. Whatever is found in other sciences contrary to any truth of this science of theology must be condemned as false.’ --- (ST, I, Q 1, a 6, ad 2).
Heliocentrists came into the world as pagan sun-worshippers and were condemned in the Scriptures. The next time they appeared they claimed they had proof for their heliocentrism (Galileo) and since then keep adding to these proofs. Nearly all in Church and State believed them.
By the end of the nineteenth century science knew there was no proof and that no such proof exists. Thus biblical geocentrism and those like Cardinal Bellarmine were vindicated, and Galileo exposed as the suspect of heresy that he was condemned as.
Now as a revelation, a dogma, a matter of faith, as St Thomas says, it has no obligation to prove any of its geocentrism. Pope Urban VIII ruled that God in His infinite power and wisdom caused the universe to move around the earth using whatever means He chose, and our human minds cannot pretend to a knowledge and certainty about nature that would limit and restrict His omnipotence.
In other words, geocentrists do not have to account how a geocentric universe slows down if indeed the days are getting slower.
Heliocentrists of course like to pretend they do know these things and thus you get the theories up on that website you posted Jehanne.