Luck.  In short, there's no validity to the idea that eggs can only be
balanced on the equinox.

This question often arises during March and September, when it is not
unusual to hear, see, or read news reports about the equinox occurring
during that month.  It is also not unusual to hear news reports being
able to balance an egg on the equinox day.  In fact many times these
reports will highlight a classroom wherein the students are shown
trying to balance eggs.  Naturally some eggs will balance and others
will not---one time, then perhaps do differently the next time.

The focus in these reports, however, seems to be on the eggs that do
balance rather than the observations from the experiment that not all
eggs balanced the first time tried, nor did all eggs always balance,
or perform the same way every time.

There are a number of problems with the idea of balancing an egg:

1. Typically, explanations about the balancing act involve gravity.
One explanation that I've heard suggested that gravity is "balanced"
when the sun is over the earth's equator.  Another gravity-based
explanation is that the sun exerts a greater gravitational attraction
on the earth on these two days.  If gravity is involved in balancing
the egg shouldn't other objects balance as well? Or is gravity
selective such that only an egg is affected on this particular day?

2. The equinox is a certain day, while the sun is actually at the
equinox point for an instant (0 degrees on the celestial equator and
12 hours within the constellation Virgo). Therefore, shouldn't the egg
only be balanced at the specific time that the sun reaches that
position?

3. If the Sun's gravity is involved, shouldn't latitude have an
effect?  For example I live at 40 degrees north.  Shouldn't the egg
lean at an angle pointing towards the sun where I live---and if so,
then it should only be standing straight up at the equator?

You can of course conduct your own experiment.  Issues to consider
when designing your experiment include, Would the same egg balance on
any other day(s) during the year?  What would be the results of
standing the same egg under the same physical conditions and at the
same time each day throughout the year?