Funny you should ask. There was a reply by 'Ask Maralyn' in the Sunday 'Parade' section of the newspaper about a few months ag that mentioned this. Apparently there is some idea that you can take fresh egg and balance it on its large side, and that it is easier to do this at certain times of the year.
The problem is that whenever such an experiment is conducted it is usually not performed with the proper controls. First, the same egg is seldom ever used throughout the year, and an eggs properties change appreciably over a long time. If different eggs are used, not enough are selected each time to average out the effects of the natural variations between one egg and another. Finally, we tend only to remember the number of successes, not an accurate count of the number of failures in each test. I would suggest that the experiment be redone with an accurate count each time of the successes and failures for each egg in a number of trials each day.
There is no physical reason why eggs should balance more frequently at different times of the year, or when the moon is at different phases.