If you have an Outpost within city borders, you can build improvements in the outpost indefinitely. Here's how it works:
Select an outpost within city borders, and add an improvement to build.
When the improvement finishes, it does not show up if you select the outpost! You can add that same improvement from the outpost screen to be built again. It DOES show up in the list of city improvements in the City Details screen.
This enables you to build unlimited Consulates, for example. Other improvements may stack as well.