Is there a way to auto run some triggers in a loop until the results are met?

You're running into a limitation: Storyline doesn’t support traditional loops or real-time conditional recursion, so using a button click to re-randomize each variable is about as close as you can get with built-in triggers and conditions.

While it's possible to handle this entirely within Storyline using triggers and conditions, the solution becomes clunky and difficult to scale if you have more than four variables. You would also end up with too many triggers, making it more complex to track and maintain. Additionally, this method introduces delays, as it relies on event-based triggers rather than true loops or real-time logic.

However, there's a cleaner workaround using a small JavaScript snippet. JavaScript can efficiently handle loops and ensure unique number generation and you can still pass those values back into Storyline variables. Let me know if you'd like help setting that up.

The trick to continuous loops is using toggle. If valueB is good, toggleC, else toggleB again. 
But, it's much easier to do this task using javascript. 

I made a row of 4 circles and displayed a variable in each: %circleA%, %circleB%, etc. These variables were text, so the same solution would work if you were randomizing fruit names or anything else.

Then attach this javascript either on page load or button click.

// Define your list as a JavaScript array
var myList = ["1", "2", "3", "4"];

// Fisher-Yates Shuffle Algorithm
for (let i = myList.length - 1; i > 0; i--) {
    const j = Math.floor(Math.random() * (i + 1));
    [myList[i], myList[j]] = [myList[j], myList[i]]; // Swap elements
}

// Update Storyline variables
var player = GetPlayer();

player.SetVar("circleA", myList[0]);
player.SetVar("circleB", myList[1]);
player.SetVar("circleC", myList[2]);
player.SetVar("circleD", myList[3]);

Actually, you can simulate your own “loop” in Storyline to keep generating random values for A, B, C, and D until they are all unique by using a motion path animation as a timer:

1. Insert a small shape (call it interval) and create a short motion path animation for it, lasting between 0.1 and 1 second (eg., 0.5)
2. Start moving interval along its motion path when the learner clicks a button.
3. Set a trigger to move interval again along the same path whenever the animation completes.
4. This creates a continuous loop effect, running every 0.5 second depending on the animation length.
5. On each animation completion, add separate triggers to assign random numbers between 1 and 4 to A, B, C, and D.
6. Also on animation completion, check if A, B, C, and D are all unique. If they are, stop (hide) the interval to end the loop.

To rerun the process, create a trigger that resets the state of interval to Normal when the learner clicks a button, which restarts the animation and loop.

This solution only requires about six triggers in total, far fewer than I originally expected, and it doesn’t rely on any JavaScript or additional layers.

Edit:
This motion path trick is conceptually similar to running this JavaScript code, though not identical. JavaScript offers more precise and consistent timing compared to motion path animations in Storyline.

const interval = setInterval(() => {
  const A = getVar("A");
  const B = getVar("B");
  const C = getVar("C");
  const D = getVar("D");

  const values = [A, B, C, D];
  const unique = new Set(values);

  if (unique.size === 4) {
    clearInterval(interval);
  }
}, 500);

I really appreciate all the assistance on this. Both in Javascript and via triggers. Thank you all for helping me out on this.