Oddly I have a coworker who bought a caramel apple and then left it in its plastic on his desk for about 4 years. We didn't photo document its decline but I should be able to recall.
After about a week the impalement point became quite unappealing. The area around the stick darkened and softened (it seemed, I didn't touch it). The rest of the skin looked fine.
After several years the caramel looked perfectly fine but misshapen and the apple had dried and shriveled inside of it.
Based on that, and my own experience, I would conclude that a refrigerated caramel apple would have about the same life as an uncarameled apple except for the core which would need to be avoided.
As for extending the life? Perhaps pour wax around the stick entry point to buy yourself a couple days?