I agree with not welding the ball on there...The temper will be permanently lost and the ultimate strength of the ball will be degraded.

Best thing to do is drill a hole through the threaded shaft just under the nut(in the fully torqued position) and keep the nut secure with a locking devide like a cotter pin or other such pin in addition to a locking washer.

is it bad when your nut becomes loose?

If you do not want to use nasty axle grease, try a shot of spray silicon into the coupler/on the ball each time you hitch up. Works like a champ.

GREASE THE BALL IT WILL FIX THE PROBLEM!

Do not, as had been said before, weld the ball to the draw bar......that would be bad........not welding good.....welding bad

You said that you are using a lock washer. If the ball is correctly torqued with a good lock washer, it should not come loose......grease or no grease. The grease is there more for reducing the wear on the ball receptacle on the trailer than anything else.

What I would recommend is getting a new ball, nut and Lock washer. Make sure the nut has an interference thread. This type of thread will allow the nut to be torqued to the proper specification, but there is no way to get it off of the draw bar short of cutting it off. The nut will not back off. Most "knowledgeable" hitch suppliers will know what you are talking about if you tell them what you are looking for.

If you just tack the nut to the shaft to the nut in a couple spots with a mig it won't hurt the temper. The mig doesn't create as much heat as a gas welder.

it was a new ball, nut, lock washer, receiver etc.

now new nut and washer drilled a pin in it, and placed a tack on the nut. tack was already done by the time everyone said not to weld. just tacked the nut and did not weld the ball to the receiver.

hopefully there will not be any 36 outlaws traveling down the freeway by themselves this year.

Loctite and pin it for extra margin