Can a helicopter be stable without moving the control inputs? I have only flown helicopters in a flight simulator (X-Plane) and I have found it exceedingly hard to fly in certain regimes (especially hovering and close to hovering) because it seems like there is no point on the controls at which I can stay and not have the helicopter start moving in a direction I want.  As a result, I wind up having to constantly move the control inputs (cyclic and yaw) in small amounts back and forth across where the stability point should be.  On flight simulator forums I have actually seen a couple of people recommend doing this.
But my question is, does this accurately reflect how a real helicopter behaves?  Is it possible to maintain a stable hover or slow speed movement in or out of ground effect once achieved without moving the control inputs much or at all?
In answer to your main question, Yes that is how they behave.
In theory in a perfectly world, there would probably be some sort of balance point, but in real life there is always something slightly affecting the helicopter causing it to start to drift.
As for how to actually fly, beyond telling you to get real lessons [don't do it], the strategy of constantly moving the controls is something sometimes called &quot;stirring the pot&quot; and in real life is generally a sign of an inexperienced pilot. With training and experience your control inputs will eventually become so small and so far &quot;ahead&quot; of the aircrafts movements that it will look like your not moving your controls. if you are not using full size controls for your sim, this may be impossible to achieve.