How long should a road tyre hold its pressure?
Do yourself a huge favor, inflate them daily. 

As they are high pressure and low volume they tend to lose air quicker than that of a tube that is low pressure and high volume (MTB). 

With daily inflation checks you will vastly reduce the instances of pinch flats, which IMO are typically the result of too low pressure. Butyl tubes, the typical tube, retain their pressure better than their Latex counterpart but still ... check regularly.

This touches on why your tyres leak down (solubility etc):
Is there a difference in having tires filled with CO₂ vs air?