That happens because subdividing deforms the surface and adds more polygons to make it smoother. Anim8or then approximates how the UVs should be placed, but there are limitations on how accurate it can get. There's a way around this...
Take a copy of the subdivided mesh, convert it to mesh, then export to .obj. Now load that .obj file into uvmapper, then save the resulting texture map. Now delete your subdivided copy and apply the texture map you made to the original low poly mesh. Convert the low poly mesh to subdivided and there you go, the texture map matches the subdivided mesh! Now you can paint on the texture map you made and apply it to the object without worrying about unexpected results. Of course, if you keep the low poly mesh unsubdivided, then it'll look funny with the subdivided texture map applied to it.
i have tried it before on another model, and it worked. But in this case (if we apply any projection like planar, spherical, and so on), it can't be done. It will work best if we keep the original uv coordinates. The problem is, an object made from scratch (by creating edge by edge to make a polygon) has no uv coordinate. The sphere, cube and other basic shapes provided by anim8or has uv coordinate, but if we delete it's vertex or edge, and try to redraw it, the uv coordinate of those vertex and lines remain deleted. The examples are below (i marked the lines i deleted with blue circles):
