Why doesn't .then() execute at all for my Promise?

I have a chain resolveof promises to run, promises will appear when complete (see code below for more context), and want my code .then()block to run...but it doesn't. Here is my code:

function notifications_for_each_in_array(iteration, the_array, error_array) {
    
    return new Promise(function(resolve, reject) {

        if(!iteration) iteration = 0;
        var error_array = error_array || [];

        var user_id = the_array[iteration];

        $.ajax({
            url: ".....my_url.....",
            type: "PUT",
            data: JSON.stringify({test: [user_id]}),
            success: function() {
                // ...
            }

        }).done(function(rez) {
            error_array.push(rez);

            iteration++;

            console.log("will stop: " + (the_array[iteration] == undefined));

            if(the_array[iteration] == undefined) { // reached the end
                console.log("Resolving...");
                resolve(error_array);
            } else {
                if(the_array[iteration] != undefined) {
                    console.log("Next: " + iteration);
                    notifications_for_each_in_array(iteration, the_array, error_array);
                } 
            }
            
            
        }).fail(function(err) {
            console.error(err);
        });
    });
}

The above function works, but when I call it using .then(), the .then()block doesn't run. In this example, I never get the alert (PS: I also tried defining notifications_for_each_in_arrayas a asyncfunction, and using await, but got the same result):

notifications_for_each_in_array(0, [0,1,2,3], [])
.then(function(res) {
    alert("here is then()"); // I never get alerted!
});