With power steering complaints such as yours where the symptom is intermittent the diagnosis is mostly guesswork in a setting such as this. You can do a few things to get to the source though.
A little about modern power steering
Many vehicles have power steering assist controls such as a vehicle speed sensors and pressure switches/solenoids that stage the level of power assist based on speed and steering load. Typically you should have full assist at lower speeds fading into no assist at higher speeds, so at startup in your driveway full assist should be present on your vehicle.
Before working through guesses you should make as many observations as possible to pinpoint things such as leaks or failing components. Look for leaks and listen for odd noises related to turning the steering wheel back and forth.
This list of possibilities is not exhaustive and is simply drawn from my personal experience. Your mileage on its usefulness may vary. ;)
Fluid is low - upon startup a car with low fluid can/will develop surges due to air being sucked through the system. Check the fluid level at your power steering reservoir. Adjust the fluid level as necessary.
Fluid is contaminated - power steering fluid will contaminate over time and properly flushing the power steering system is a commonly neglected maintenance item. Depending on driving conditions and fluid quality the contamination can vary from soot developing in the system to goopy sludge caused by moisture. Use a turkey baster to draw out some of the fluid when it is cold and determine whether it is contaminated. The fluid should not be black/opaque. Check your owner's manual for the recommended power steering service interval and do this first if you are having a problem. If the fluid is contaminated then putting off the flush could lead to much more expensive repairs.
The filter is clogging up - this is usually a byproduct of condition #2 and typically the clogging filter is what gets a person to pursue fixing their car's problem. Some vehicles have an inline filter where on others there is a screen built into the reservoir that captures contaminants. Replacing or cleaning the reservoir should be part of a good power steering flush. If your reservoir is clogging then negative pressure on the system can cause wear problems on other components.
The power steering pump is leaking/failing - A failing power steering pump often is visibly leaking. Leaking pumps fail to operate properly due to air/contaminants entering through the bad seal or lack of sufficient operating pressure caused by fluid escaping the seal. (depending on which seal is leaking) Premature failure of a power steering pump can also be experienced when certain power steering fluid types begin to break down or abrasive contaminants are carried through the system. The failing pump is going to get your attention when it begins to buzz, rattle or whine.
The control body is failing - There is a controller consisting of orifices and valves that allows fluid to flow based on need and rack load. This control body has highly precise tolerances and will wear out or clog due to fluid contamination or fluid failure. This unit is typically part of the rack and pinion assembly. If you hear a whine or jitter coming from under the vehicle and in close proximity to where the steering yoke meets your power steering rack then this could be the problem.
Other unknowns - The problem could be none of the above. Kinked or collapsed hoses, electrical problems and even solid state device failure is not out of the question. Anomalies across designs exist and a specialist with your car maker might be the best place to find advice.