The fall of Humpty Dumpty

Humpty Dumpty is a meditation on the fleeting nature of power and the risk that comes with any position of authority. 
The fall that Humpty took was only fatal because he had ascended to such heights.  
All the Kings Horses and all the Kings men were in fact his army, capable of defending him from outward threats but impotent against the ones inherent to his position of King and the envy it inevitably inspires among those closest to him.

Consider that if he had not been alone on his wall, others would have been nearby to reach out and catch him.  But balanced at the top, there was no help. Only a desire to push or pull him down so that someone else could enjoy the view.   It ultimately draws parallels to the fate of King Charles II.
...this is all, of course, completely made up.   And yet, it can be argued to be a correct meaning.

The fact is the nursery rhyme was probably never really intended to teach lessons. As has been pointed out it does work as a riddle, and that's purpose enough.  But according to one school of thought, artistic intent is less important than the experience of the audience in interpreting the meaning behind any work.
~Dean Kuch