What causes trade routes to be broken?

From your image I can tell two things:

1. That your two cities both have a harbor.
2. That your two cities are still actually connected.

You can tell that they are connected by looking at Shanghai. Right underneath the city name for Shanghai, there's a small black circle with three yellow dots . This icon means that you have a trade route with your capital city.

The reason you received a message that the trade route was broken, was most likely because you built a harbor in both cities. When you do so, the game changes your trade route from by land/road to by sea. It is a bit misleading because this "a trade route has been broken" prompt still comes up, and is technically correct, but in reality your trade route is just changing from via road to via sea.