The function copyobj(h,p) copies objects listed in h to a new parent, p. When your code is run, the error message indicates, "Axes cannot be a child of Axes." This is because you cannot assign one axis as a child to another axis. Rather, you should copy the axis to a new figure.
Here's the correct way to do that:
f2 = figure();
ax2 = copyobj(ax1,f2);
[UPDATE]
To copy objects from one set of axes to another, you must first get handles to all of the axis children and then copy that list of handles to an existing axis. Here's a demo that follows the code in your question.
ax1Chil = ax1.Children;
copyobj(ax1Chil, ax2)
In your case, even though the axes you're copying from are polar axes, the data are actually plotted in Cartesian coordinates. So you'll copy the objects to a cartesian plot (middle figure below).
ax1Chil = ax1.Children;
figure;
ax2 = axes;
copyobj(ax1Chil, ax2)
axis equal
rectangle('Position', [-50 -50, 100, 100], 'Curvature', [1,1])
If you add the object to a polar axis, the (x,y) coordinates create a completely different pattern (right figure below).
ax1Chil = ax1.Children;
figure;
ax2 = polaraxes('ThetaTick', -150:30:180, 'ThetaLim', [-180, 180]);
copyobj(ax1Chil, ax2)
The image below shows [original, Cartesian axes, polar axes].
