How long should a road tyre hold its pressure? How long should a road tyre be able to maintain a pressure of around 100psi, and what factors are likely to reduce this time?

Background:

My tyre pressures are consistently dropping to around 60psi after about a week (three commutes, total ~50 miles), which makes the bike feel sluggish and less responsive.

I've only recently got a road bike, but I've always had mountain bikes - they've always held around 30 psi for weeks and weeks with no problems. I'm wondering if it's the higher pressure that's causing my tyres to need inflating more frequently, or something else?

This answer to another question, and some other answers I've seen suggest that you should check your tyre pressure every day, but is this to be cautious or are you likely to actually have to inflate your tyres every day?
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?