Javascript function only runs once? Attempting to use same function multiple times

First, you need to understand why it doesn't work for you and then find a solution.

The problem is that, you are using the same element ID in two separate elements, this is not strictly forbidden and will not throw you any errors, but it points to a wrong implementation.

When you are trying to select elements with the ID getAllUsers using jQuery, it knows that there should be only one such element, so it selects only the first one. Any other elements with the same ID are ignored. That's why it worked only for the first one.

Now, let's try to find solutions.

One solution, as Miroslav Glamuzina suggested is correct and works, but not flexible enough.

Another solution would be using a selector that selects multiple element which is not an ID. The best option is to use element's class, that will be unique for your two (or more) select elements. So if you want to add another one in the future, you don't have to touch the JS code, but only the HTML part.

You can do something like this:

HTML

<select class="select2 getAllUsers" name="user" required>
    <option selected="true" disabled="disabled">Loading Users...</option>
</select>

<select class="select2 getAllUsers" name="user2" required>
    <option selected="true" disabled="disabled">Loading Users...</option>
</select>

(Note that I also changed the name attribute of the second select, to prevent issues in the future)

JavaScript

(function getAllUsers() {
    $.ajax({
        url: 'staff/getAllUsers.php',
        success: function(data) {
            $('.getAllUsers').html(data);
        },
        complete: function() {
            // Schedule the next request when the current one's complete
            setTimeout(getAllUsers, 5000);
        }
    });
}());

WARNING!
If you are planning to use this script publicly, you should pay attention on the security issue in this script.

This script is opened for XSS attacks. Because, you are requesting a remote content and applying its content as HTML without any data validations nor escaping.

I would suggest in your case, to generate a JSON in the PHP script, with the list of users and all the data you need, then on the JavaScript, create option elements using the data from the JSON list.

You should do something like this:

Let's say that this is the JSON received from staff/getAllUsers.php:

[
    {"id": 14, "name": "User 1"},
    {"id": 16, "name": "User 2"},
    {"id": 17, "name": "User 3"}
]

JavaScript:

(function getAllUsers() {
    $.ajax({
        url: 'staff/getAllUsers.php',
        success: function(data) {
            try {
                const list = JSON.parse(data); // Parse JSON from string to object
                const selectEl = $('.getAllUsers').empty(); // Clear the content of both `select` elements
                for ( let i=0; i<list.length; i++ ) { // Loop through each item in the JSON array
                    $('<option />') // Create an `option` element
                        .attr('value', list[i].id) // Set attribute `value` to `option` element
                        .text(list[i].name) // Set `option` text (this function also escapes any special characters, which prevents potential XSS attacks)
                        .appendTo(selectEl); // Add `option` element to both `select` elements
                }
            } catch (e) {
                // Report any errors with the JSON parsing process to the developer console.
                console.error(e);
            }
        },
        error: function(jqXHR, textStatus, errorThrown) {
            // Track any errors received from the server for debugging purposes
            console.error(textStatus, errorThrown);
        }
        complete: function() {
            // Schedule the next request when the current one's complete
            setTimeout(getAllUsers, 5000);
        },
        dataType: 'json' // Expect a `json` back from server
    });
}());

I hope you can learn something from this.
Good luck!