What you seem to have is a classic high resistance connection either between the wire and the connector terminal (unlikely) or between the terminal and the spade from the headlight bulb (likely). The terminal (inside the connector) is made of tin coated brass. It is intended to act like a spring and apply continuous pressure to the spade on the bulb. Due to vibration, it may have relaxed its connection, causing a high resistance connection. This leads to high temperature and melting of the plastic connector body. Once this happens, it anneals the brass and ruins the terminal for good.
The bad news is that there is no easy way to fix it. I am sure Suzuki will be happy to sell you a complete wire harness in order to get a new connector. Better yet, you should be able to find one at a salvage, you can splice it in place of the original. I think most, if not all, motorcycles use the same connector. Just take your headlight and confirm a match before purchasing a new part, and you should be on your way.
Be sure and clean the spade on your bulb to remove any carbon build up to prevent the same problem again.
Good Luck,