The Loadstone description reads as follows (emphasis mine):
Curse. The stone is cursed, but its magical nature is hidden; detect magic doesn’t detect it. An identify spell reveals the stone’s true nature. If you use the Dash or Disengage action while the stone is on your person, its curse activates. Until the curse is broken with remove curse or similar magic, your speed is reduced by 5 feet, and your maximum load and maximum lift capacities are halved. You also become unwilling to part with the stone.
Unlike most cursed objects, this does not require any attunement. So just being on your person is enough. Since the character does not attune, there is a "trigger" to the curse. In this case, it is when the character uses the Dash or Disengage action. But Dash and Disengage are not one-time things like attunement. One or both can be done multiple times in a minute.
So does each trigger compound the curse, reduce speed and max capacities halved, or is the character cursed only the first time they perform that action and that’s it?
The spell doesn’t specify "the first time you…", it just says "it activates". But things can be activated repeatedly so that is not a disqualifier.
I could see a situation where, not knowing that the stone is the issue (since detect magic doesn’t show it as magical) a rogue keeps disengaging and dashing to get away from a foe until they are incapable of movement and are crushed by their own equipment.