updating the values in widget (properties) not working

Do you mean values and properties in the Widgets application? If yes, you need to re-add the widget on given page. The changes are not distributed automatically as the widget on the page is a separate instance and it is saved either within the document or page template configuration.

We have added a widget in a page and we click the configure and change the value in editor window. On click of "Save and close" button, the new values are not updated or shown in the page.

OK, this is something different then.
So, what version, hotfix and development model are you using?
Are there any errors in the Event log, browser console?
Does it happen to all widgets, even the out of the box ones or certain widgets only?

There are no console errors and errors in Event log. We are using Kentico version 12 (licensed one), portal Engine.

Currently we are using custom widgets, with layouts (no code behind)and it does not happen to all widgets.

we noticed this happens, * when there are more number of properties available for a widgets. * when we are using Richtextbox property * Properties in page types too.

Does it happen also to the out of the box widgets? Keep in mind that we are not aware of your custom widgets, the underlaying web parts and the code logic. So, I need steps and description how to reproduce the issue using clean, non-customized project and using out of the box widgets and web parts.

We cloned the "editable text" webpart and no addition properties were added. On updating the data , its not reflecting in pages and this happens intermittently.

Why did you cloned the web part and what changes were made? Are you able to reproduce the issue with the out of the box widget and web part? If not, then review the changes you have made and debug your code.