Why are my overlapping meshes rendered in the wrong order?

I have created a mesh by specifying vertices and triangles by hand. The mesh is updated at runtime. I am using a Particles/Alpha Blended shader from the standard shader selection in Unity.

Below I have a screenshot of the a green and red mesh with a bit of overlap. However, depending on the camera orientation in the scene view, sometimes Unity draws the meshes in the correct order (right image), but sometimes it gets the order between meshes wrong (left image). Between these two, there is only a slight camera orientation change in the sceen view (right mouse button drag). The same problem appears in the game view, where sometimes the meshes pop back and forth between correct order and wrong order.

What is the cause of this and how can I fix it?