At rest position, the mechanism which prevents the clamp from opening no longer provides enough friction, causing the clamp to move freely in this direction, and making it impossible to use one handed in a vertical position. It became more or less unreliable. However, once tightened, it looks like it can still hold the pressure. Can I do something to make it work better ?
Yes in this case it could be fixed easily.
This piece of steel is the one that prevents the clamp from opening, so it makes sense that over time it will bend in this direction. I bent it back to its original shape, and put everything back together;
Nothing else was needed in my case. It's now working properly. I just checked another clamp from the same manufacturer, which is just a bit shorter, and it had already started to suffer from the same problem. Maybe they do it on purpose (planned obsolescence.. ).
I find these clamps to be reasonably unreliable - in my experience they all eventually fail as you describe.
One of the causes is that the bar becomes too smooth for the clamp to get sufficient friction. In this case you can try filing/roughing up the bar at the front and back to give it something better to grip on to.