Material Changing at Run-Time on Static Batched Objects

Since updating to the latest version of Unity, a number of bizarre things have been occurring in our game.

One easily reproduced issue is that some objects flagged for static batching are having their material seemingly replaced at run-time.

Here is a building as it appears in the editor.

Once the game is running, it changes to look like this:

It appears that the concrete material is being swapped for the material of the swampy water. If I un-check the building object as being static, the object shows up normal at run-time.

Any ideas as to what might be causing this? It only seems to occur with objects marked as static. Since they're static, I can't manipulate them to get more info while the issue is occurring, and if I stop running the game or make them non-static, the issue does not occur.