It's possible the threads have been damaged and the lockring won't hold no matter how tight you crank on it. Loctite may help, but failing that, you'd need a new hub.
OP... I recently went to my co-op intending to put a suicide setup on the freewheel side of my fixed/free hub. The guy in charge said quote "sorry but I can't let you do that here. There's a reason they call it a suicide hub." He added that any skid will put way more force on the cog than you can put with a chainwhip.
I went home and rotafixed the thing as tight as I could then went for a ride. A few skids confirmed the co-op dude's remarks.
Basically... if a lockring is not reverse threaded, it's not a lockring. It's just extra threads twisted onto the cog. The Loctite red solution would be the only one I would trust if I'm not running front and rear brakes.