Local servers means a server in different countries like in nepal np.archieve.ubuntu.com How often are they sync with the main server to update the packages and ISOs ?
Here is a list of mirrors where it also mentions how up to date it is.
How often are the local servers of ubuntu updated?
It depends on the local server. They pull the software in at their convenience.
But specific to Nepal (you have 1 mirror): Nepal Telecom is one day behind for Yakkaty Yak and up to date for all other releases.
If you look at my country below it (Netherlands; 16 mirrors) it shows a mix of "up to date", "one day behind", "1 week behind" and even "unkown".