How to extend holding time for poached eggs?
Some data:

Egg whites start coagulating at 150F.
Egg yolks start thickening at 150F and become solid at 158F or so.
The danger zone for bacteria is between 40F and 130F.  

What this means is that your perfect poaching temperature is going to be somewhere around 150F to 155F depending on how firm you like your eggs. At these temperatures bacteria can't grow and if held at this temperature the eggs will never overcook. Over time the yolks will become thicker but it takes many hours.

The serious way to do this is with a sous vide setup that electronically controls the temperature of a water bath.

A cheaper method is what jbarker2160 referred to as the beer cooler method.


Pour 155F water into a cooler (or hotter and let it cool with the lid
off)   
Add the eggs in their shells.   
Put the lid on and let them
cook forever. They won't overcook.


They can be served out of their shells. The shape is different than poached but IMO better.

You do need to make sure your cooler doesn't ever dip below 130F very long before serving or you risk bacteria growth.