As we do not have access to your website we can not give an exact response to your question. There might be cases that the old version of the theme does not have the ability to have the automatic updated due to the change to the API, but yours is 5.2 which is not that old, but there might be server factor preventing you to access our servers.
I suggest that you follow the steps of a manual installation at the moment, and if in the next update you see no update notice then get back to us in a new thread to follow up.
Please do not reply here as you are not the original poster of the thread and in it is better to focus on your case on a separate thread and if needed you will give us your website credentials via Secure Note which is visible to the original poster and you can not do it here.
Thank you for your understanding.