The trajectory of this post has really evolved! I thought I understood that the problem was that the jaws were loosening on the tenon, but the conversation now seems to be suggesting that the problem is that the entire chuck is unscrewing from the lathe spindle.
The question related to the PSI Utility Chuck - this is a basic tommy-bar chuck that has a native 1"x8pti thread, but that is supplied with a 3/4"x16tpi adapter for use with minilathes. The photograph in the original post shows the No 2 jaws that come with the chuck (basic 50mm jaws that are neither flat or dovetail - instead, there is a ridge at the edge of the jaw that grips the tenon). It does not have a grub screw to lock the adapter into the chuck body, or to lock the chuck to the lathe spindle.
I think we need a better explanation of the problem from the original poster. Is the problem that the jaws are losing their grip on the tenon, or is it that the chuck is unscrewing from the lathe spindle? And I would add another question - is this a new chuck or has he been using it for some time? And if it is 'experienced', is the problem he is reporting something that first materialized when he used it to turn a bowl from a composite wood-plastic blank?
As Charlie and Glenn have correctly said, IF the problem is that the chuck is unscrewing from the lathe, then it is almost certain that the OP running the lathe in reverse - the normal rotation of a lathe tightens the chuck to the lathe spindle.
However, it the problem is that the jaws are actually losing their grip on the tenon, then I still suspect that vibration is causing the jaws to loosen.
I've been successfully using the same chuck for about seven years; I've noticed that the jaws sometimes loosen when used in expansion mode (with a mortise mount), but I don't recall having the jaws lose their grip in compression mode (with a tenon). I am acutely aware that the chuck can unscrew itself from the lathe spindle if I stop the lathe without first reducing the speed - I've had to jump out of the way a couple of times when it came off the lathe entirely avoid having it land on my foot!
The other possibility is that if this is a new chuck, it is possible that it is defective.