To change the position of the x label, store the handle to the xlabel, then change its position property. By default the axis labels are in 'data' units. If you want to move the x label down, you'll want to subtract from the y-coordinate of the x label position.
xlh = xlabel('x label');
xlh.Position(2) = xlh.Position(2) - 0.1; % move the label 0.1 data-units further down
In this demo below, the x label is moved down by 10% of its distance to the axes. Note that the x label position could have a positive or negative y-value so abs() is needed in order to always offet toward -inf.
figure
axh = axes;
xlh = xlabel('x label');
xlh.Position(2) = xlh.Position(2) - abs(xlh.Position(2) * 0.1);
Caution: if you move the x label too far, it may no longer be visible.
