Different brands may use different materials for the step-up/step-down rings. I used to have both the Raydawn and B+W 72->77 step-up rings and they are worlds apart. Raydawn is cheap and around $10+, feels so light I am wondering if it is made of plastic. OTOH, B+W costs me around $30, feels solid because it is made of brass and has knurls at the front to help with gripping when (un)screwing the ring.
I have not heard of rings unscrewing themselves but more often on stuck rings/filters.