Losing water pressure in water hose while washing vehicle
There are a few reasons this can happen.

Other uses of water + small lines

Depending on the size of pipes and the way it's plumbed in, it could happen if something/something else in your house was using water (dishwasher, washing machine, shower). This happens a lot in subdivision homes (which are built using the bare minimum amount of money required to meet code), where all the branch lines are 1/2". 

Hose clogged

You can also check the hose when this happens: disconnect it from the hose bib (aka spigot), and see if that has a reduced flow as well.

If it doesn't, there may be something clogging your nozzle or hose. 

Pressure regulator

You may also have a pressure regulator on your house (see pic below). These can have trouble if the supply pressure is below what they're set at -- I'm not 100% sure what happens but I'd bet it would reduce the pressure like what you've said. 



They can also get clogged with debris (though unlikely with city supply) and sometimes fail for no apparent reason (though again, unlikely).