I recently ran into a problem while using Entity Framework with Structuremap. The issue was mainly present while making concurrent calls to Web API endpoints, because they were all asynchronous. After a lot of investigation and looking around for various examples (mainly using other IOC containers), I came up with a solution.
My particular app is built to be somewhat modular, so this may be more complex than some need, but hopefully still helpful
This is picked up by StructureMap on application startup as another "registry."
public class EntityFrameworkRegistry : Registry
var config = DataAccessConfig.GetConfig();
var dbConnName = config.Connection.ConnectionStringName;
Basically, I'm getting my connection string (name of the connection string or the actual connection string itself) from the Web.config and injecting that into to the constructor of MyDataContext. This seems to properly create the context so it creates a new instance per request.