Are you working with Windows Azure Logic Apps inside Visual Studios and seen an error like this after you deploy?

The API connection '/subscriptions/{Subscription ID}/resourceGroups/{Resource Group Name}/providers/Microsoft.Web/connections/sql' is a connection under a managed API. Connections under managed APIs can be used if and only if the API host is a managed API host. Either omit the 'host.api' input property, or verify that the specified runtime URL matches the regional managed API host endpoint 'https://logic-apis-westus.azure-apim.net/'.

What I have found is the Logic App gets a little sticky to a Region.  It seems to like the initial region you set when you first created the Logic App.  Most of the shapes inside a Logic App are internal API calls to Microsoft hosted services.  This ends up looking like this in the JSON:

"host": {
              "api": {
                        "runtimeUrl":
https://logic-apis-eastus.azure-apim.net/apim/sql},
                         "connection": { "name": "@parameters('$connections')['sql']['connectionId']"}}

As you can see the eastus is set in the runtimeUrl of the internal API call to the SQL API.  When this is deployed to another region, at present Visual Studio does not replace this value with the correct region. 

So what happens when you deploy to another region?  Well these values get sent as-is. 

If you run the Logic App you will get an error message like seen above. 

To fix this issue it is simple, once you deploy the Logic App into a new region open it inside the Web Portal and Save It.  You do not have to do anything else.  This will adjust the runtimeUrl values to the correct region.

Happy Logic Apping!