We have used a Date Field in one of our component's dialog. When author selects a date and save the changes, it gets saved in jcr but whenever authors reopens the component dialog it doesn't displays the previously authored date. Tried inside multifield as well and found same behavior.
AEM version - 6.1
Do you have a component specific client libs written out for the date field? Can you upload a screenshot of the properties so we can take a look at how the date value is stored? As a property or as a node?
Date types are stored fine when the dialog re-opens. I know this document is not listed in the Experience League under the API category for some reason - but it shows you how to work with dates in dialogs:
There are some OOTB components in AEM 6.1 that has a datefield widget in the Geometrixx site. I would recommend reviewing them to see how to configure the widget.
Also, I would disable any overlay code to ensure that these are not interfering with the way the datefield widget function.