As @MieszkoZ pointed out in his answer, this problem could be fixed by adding new Supported Agent to the Navigation System in the Project Settings:
With this, I can restart the Editor and the RecastNavMesh.AgentRadius value in the level persists.
Also, there is Nav Data Class variable in the Supported Agents so I assume you can create your own RecastNavMesh class and add it here if you want to change some other NavMesh variables.