3d scatter points at the back overlap points at the front

I am preparing 3d plots with matplotlib and I am having a really weird behavior with multiple datasets. I have two datasets that describe basically two shells in 3d: one inner shell and one outer shell. To plot them in 3d I do:

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')    
ax.scatter(outer_z[:n], outer_x[:n], outer_y[:n], c='black', marker='.', lw=0)
ax.scatter(inner_z[:n],  inner_x[:n], inner_y[:n], c='red', marker='.', lw=0)

ax.set_xlabel("Z")
ax.set_ylabel("X")
ax.set_zlabel("Y")

ax.set_xlim([-5,5])
ax.set_ylim([5,-5])
ax.set_zlim([-5,5])

(the order of the axes are just for perspective purposes). When I save the figure, however, I don't get two shells:

I get one layer over the other, with the points that are clearly in the back appearing in front. You can see on the pictures that some points of the outer shell that should be behind the inner shell are plotted in front of the inner shell. This is really annoying, because it does not pursue the "plot in 3d" purpose. Does any one have an idea on why is this happening and how could this be solved?

thanks you so much for your explanation :) I thought it could be something like that indeed. But I forgot to say in my question that the same thing happened no matter the order of the ax.scatter commands, what is pretty weird. I found out before reading your answer that that does not happen with the ax.plot command. Therefore, I replaced:

ax.scatter(outer_z[:n], outer_x[:n], outer_y[:n], c='black', marker='.', lw=0)
ax.scatter(inner_z[:n],  inner_x[:n], inner_y[:n], c='red', marker='.', lw=0)

by

ax.plot(outer_z[:n],  outer_x[:n], outer_y[:n], '.', markersize=1, color='black') 
ax.plot(inner_z[:n], inner_x[:n], inner_y[:n], '.', markersize=1, color='red') 

And I got the following picture:

which works for me. I know, however, that if I change the point of view I will have the red shell appearing on top of the black one. One problem I found later was that the .plot function does not have vmin and vmax arguments (as the .scatter one), which makes it harder to define the color as a gradient starting in vmin and vmax...