If using a physical key:

Mitsubishi includes a utility called MELSOFT License Manager.

Rarely, the license check fails if you are using Remote Desktop (RDP) or have switched display adapters. Try launching GT Designer directly on the local machine (not over RDP).

If you have a network license (floating license), ensure the server hosting the "MELSOFT License Server" is never put to sleep. Use a static IP address for that server.