I think that the colorbar and axes positions aren't really stable at the point that you're changing the Position. Possibly because the figure is Visible='off', but I'm not sure about that. You can probably get things to be a bit more stable if you insert a drawnow after call the colorbar.
But, when I'm doing an animation like this, I usually pull the plotting function out of the loop and use the returned handle to update the data. The reason for this is that then all of the axes positioning is only happening once, not every frame. That tends to make things a lot more stable.
For your example, that might look something like this:
set(gcf,'visible','off')
mov(pf) = struct('cdata',[],'colormap',[]);
% Initialization
h = surf(X(:,:,1),Y(:,:,1),P(:,:,1));
grid('off')
xlabel('x(m)');
ylabel('y(m)');
zlabel('|Grad(P)| (Pa/m)');
axis([x0 xf y0 yf z0 zf])
view(50,45)
colormap jet
caxis manual
caxis([z0 zf])
cbar = colorbar;
ax = gca;
axpos = ax.Position;
cpos = cbar.Position;
cpos(3) = 0.5*cpos(3);
cbar.Position = cpos;
ax.Position = axpos;
% Animation
for p = 1:pf
h.XData = X(:,:,p);
h.YData = Y(:,:,p);
h.ZData = P(:,:,;);
titleInfo = cell(3,1);
titleInfo{1,1} = '|GradP| vs x and y';
titleInfo{2,1} = ['U = ',num2str(u,'%3.2f'),' (m/s)'];
titleInfo{3,1} = ['t = ',num2str(t(p),'%3.2f'),' (s)'];
title(titleInfo);
mov(p) = getframe(gcf);
end
close('all')
set(gcf,'visible','on')
