When Work Item Type (WIT) links are not migrating as expected, you need to determine if you are using a narrow query (see Why you should avoid narrow queries! Q&A-32 for more information), which could result in some or all of the links getting left behind during a migration.
Looking at the illustration below we have three work item types (blue:1,3, red:3 and orange:2,4). If we configure a migration session that specifies a WIQL query that only migrates items of type blue and orange, only the links between these two types are preserved as shown on the right. As work item type red is not migrated, the links 3, 4, 5 and 6 are not migrated because there is nothing to point them to on the target system.
The constraints of the tooling also specify that the migration of Test Cases with shared test steps are not supported. Investigate tools such as Visual Studio 2010 Test Case Import Utilities if you have this requirement.
Hint : Before you run a migration in production, please test the environment, the configuration and the migration in a test environment first!