If you are noticing a fall in tire pressure after a few minutes and then it stabilises (so therefore not punctured or leaking), it is quite possibly a phenomenon called Adiabatic Heating which occurs when the pressure of a gas is increased from work done on it by its surroundings;
As you inflate the tire you compress the gas in the pump / tyre / inner tube, this in turn increases the temperature of the gas in the pump / tyre / inner tube which then causes the gas to expand which in turn causes the pressure to increase.
(Basically - the greater the pressure increase - the greater the temperature increase - the greater the expansion of the gas - the greater the pressure increases...)
I hope that makes sense.
What will then happen; you start riding, after a few minutes the temperature of the gas in your tires cools to the ambient temperature and the pressure in the tire falls.
Don't get me wrong we are only talking a few degrees, but because of the pressures involved & the volume of the tyres it will be noticeable.
Andy
PS - Those who use CO2 inflators will notice that the CO2 cylinder cools when they fill they inflate their tyre - the reverse of the logic applies (the pressure in the cylinder falls rapidly causing the remaining gas in the cylinder to cool - this in turn causes the gas to contract thus causing the pressure in the cylinder to fall further)