In view Model add Observable Collection with Order Items, this collection should notified view about changes in it.

public class Book Explorer View Model : Dependency Object // book Provider.

This may not be the cause of your problem, but I'd recommend looking over your code-behind to ensure that the variable is not getting re-instantiated.

but for some reason the data isn't updating in the UI (new items aren't added visibly in the UI).

I can then remove an item from the m_Variable List collection, and it does not disappear from the List Box. I used the same XAML successfully in a test application; however, I was able to replicate the issue you are experiencing by re-instantiating the m_Variable List variable.

When the m_Variable List is given a new instance, or pointed to a new object, it is not reflected in the List Box because the control has its own reference to the data.

However, if I go view the List Box, updates seem to stop at that point. The problem is not in the XAML that you have provided.

I have spend a lot of time on Stackoverflow and i know there are many related questions but i could not find answer .

Whats bugging me is that , if it works when i add values in the constructor then why it doesnt work if i add values in the some method .

I tried to debug binding, but I have too many bindings to find the error. Listbox: - that is just a list, which does not issue any notifications to bound properties that its contents has changed.

Hence, your listbox cannot possibly know when the collection has changed.