That's a size-of-data operation, and those can take quite some time if the table is large. In a way, it is sort of silly to have a query timeout for operations that can take long time. Then again, you could also say that it is a wake-up call that maybe this is something you should not run from a UI.
You can think of things like the Table Designer as a tri-cycle. It may help to get you started, but as you grow up, you move over to a proper two-wheeled bicycle. That is, you learn to use DDL (Data Definition Language.) In this case, it is simple:
ALTER TABLE tbl ALTER COLUMN col nvarchar(50) [NOT] NULL
I've put NOT in brackets, since I don't know the current nullability for the column. But you need to repeat it, or else it may change.