One possible approach is:

for(var y=0 ; y<=23 ; y++)
{
    makeRequest(y);

}

function makeRequest(y){
    var AjaxRequest17 = null;
    AjaxRequest17 = getXmlHttpRequestObject(); // function to create the request

    if(AjaxRequest17.readyState == 4 || AjaxRequest17.readyState == 0) 
    {
        AjaxRequest17.open("GET", "ajax.php?q=17&SectionID=" +encodeURIComponent(SectionID)+ "&day=" 
                +encodeURIComponent(document.getElementById("cboDays").value)+ "&TimeSlot=" +encodeURIComponent(y), true);

        AjaxRequest17.send(null);

        AjaxRequest17.onreadystatechange = function()
        {
            if(AjaxRequest17.readyState == 4) 
            {
                var content = AjaxRequest17.responseText.toString();
                /* Process server response and update display accordingly. */ 
                document.getElementById("timeDiv"+y).innerHTML = content;

            }/* end if */            
        }/* end function */            
    }/* end if */            

}

I have revamped the entire code to achieve the desired functionality without utilizing asynchronous = false, thus preventing browser freezing:

function handleAjaxRequest(url, callback) {
    var request = null;
    if (window.XMLHttpRequest) request = new XMLHttpRequest();
    else if (window.ActiveXObject) // for IE
    {
        try {
            request = new ActiveXObject("Msxml2.XMLHTTP")
        } catch (e) {
            try {
                request = new ActiveXObject("Microsoft.XMLHTTP")
            } catch (e) {}
        }
    } else {
        throw ("Ajax not supported!");
        return;
    }
    request.open('GET', url, true);
    request.onreadystatechange = function () {
        if (request.readyState == 4) {
            if (typeof (callback) == "function") callback(request);
        }
    };
    request.send(null);
    return request;
}

function fetchData() {
    var value = parseInt(arguments[0]);
    if (value > 23) {
        alert("All data loaded up to 24!");
    }
    
    var url = "ajax.php?id=16&AreaID=" + encodeURIComponent(AreaID) +
        "&month=" + encodeURIComponent(document.getElementById("cboMonths").value) +
        "&TimeSlot=" + encodeURIComponent(value);
        
    var customCallback = Function('request', 'document.getElementById("divTime' + value + '").innerHTML =' +
        ' request.responseText;' +
        'fetchData(' + value + ');');
        
    handleAjaxRequest(url, customCallback);
}

fetchData(0);

To improve the efficiency of your ajax calls, consider setting them to be synchronous by using the asenkron false parameter like this:

for(var y=0 ; y<=23 ; y++)
    {
        AjaxRequest17 = null;
        AjaxRequest17 = getXmlHttpRequestObject(); // method implementation for creating the request object

        if(AjaxRequest17.readyState == 4 || AjaxRequest17.readyState == 0) 
        {
            AjaxRequest17.open("GET", "ajax.php?id=17&AreaID=" +encodeURIComponent(AreaID)+ "&month=" 
                    +encodeURIComponent(document.getElementById("cboMonths").value)+ "&TimeSlot=" +encodeURIComponent(y), false);

            AjaxRequest17.send(null);

            AjaxRequest17.onreadystatechange = function()
            {
                if(AjaxRequest17.readyState == 4) 
                {
                    var responseText = AjaxRequest17.responseText.toString();
                    /* Process and display data received from the server. */ 
                    document.getElementById("divTime"+y).innerHTML = responseText;

                }/* end if */            
            }/* end function */            
        }/* end if */            

    }/* end for loop */  

Load content sequentially using ajax

Here is a basic ajax function that works on modern browsers like Chrome, Safari, IE10, Android, and iOS.

function ajax(url, callback){//url,function
 let xhr = new XMLHttpRequest;
 xhr.open('GET', url);
 xhr.onload = callback;
 xhr.send();
}

This code demonstrates how to load content sequentially:

let current = 0;
const total = 23;

function handleResponse(){
 document.getElementById("divTime"+current).innerHTML = this.response;
 current++;
 if(current < total){
  ajax('url.php?id=' + current, handleResponse)
 }
}

ajax('url.php?id=' + current, handleResponse);

This approach ensures previous ajax calls are not overwritten.

Having multiple ajax calls simultaneously is not recommended.

If you still need to make multiple ajax calls at the same time, create separate instances of XMLHttpRequest.

 let ajaxCalls = [];

 ajaxCalls[0] = new XMLHttpRequest;
 ajaxCalls[0].CUSTOMID = 0;
 ajaxCalls[0].open('GET', 'url.php?id=' + 0);
 ajaxCalls[0].onload = function(){console.log(this.CUSTOMID, this.response)};
 ajaxCalls[0].send();

When it comes down to it, the key factor is the asynchronous nature of Ajax calls. Every Ajax request must be kept alive until it either completes or fails.

In your original code, only one Ajax request context is used. The loop initiates the first request, but then immediately replaces its context with the second one long before the first request is processed. This results in a situation where when the server responds (a few milliseconds later), there is no handler left on the browser side to handle the response (except for the 24th one).

Your workaround involves creating different contexts and callbacks for each request by storing them in separate closures within your global function.

However, this approach leads to firing off a barrage of 24 Ajax requests simultaneously to the server, potentially causing unnecessary overhead or even crashes if your PHP script is not designed to execute concurrently for the same request. Additionally, synchronizing your code upon completion of these requests will prove to be challenging.

Here is the method I implement for my own applications:

// --------------------------------------------------------------------
// Ajax lite
// --------------------------------------------------------------------
function PageCache (target, void_contents)
{
    // implementation details here...
}
// rest of the code...

In your scenario, you can utilize it as follows:

Firstly, some cleanup steps:

// compute_id() function definition should go here...

var Ajax = new PageCache (
     'ajax.php?$',          
     'error loading data'); 

1) simultaneous requests (not recommended)

// for loop code block goes here...

2) sequential blocking requests (very bad, don't do it unless absolutely necessary)

// another for loop code block goes here...

3) sequential non-blocking requests

// final code snippet goes here...