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Bill.  I’ve tidied up my original explanation.  This is my final attempt (well, until my gyros arrive from eBay)

If the nominally vertical spin axis of the spinning gyro is displaced out of the vertical for any reason, gravity doesn’t cause the gyro to topple further or swing back into the vertical as might be expected from either a top heavy or bottom heavy gyro.  Instead, the gyro precesses like a child’s top such that its spin axis follows a path akin to moving around the outer surface of a cone with the apex of the cone coinciding with pivot point of the gyro. This conical movement awakens fresh forces upon the gyro.  Typically, the pivot point will attempt to follow a circular path of small radius within its cup, as opposed to the zero radius of a gyro with a perfectly vertical spin axis.  Therefore, there will be a tiny frictional force in the opposite direction to the one in which the pivot point is trying to walk.  This is akin to pulling at the bottom of the spin axis, and due to the same process which causes a spinning gyro to precess when disturbed from the vertical, will cause the gyro to gradually re-erect itself. 

Put more simply, vertical force, gravity, can only cause a spinning top to precess in the horizontal plane.  For the gyro to precess in the vertical plane, you need to apply a force which is both in the horizontal plane and in the correct direction, e.g. friction at the pivot point due its attempt to travel around a tiny circle inside its cup. DaveP