When I do the form post I get an error with the first 2 options, even though they show the calendar input select as updated and the format is exactly the same:
It seems from the screenshot that you are using the date picker only. Check whether your database field type is date or datetime as the value may not match with the field type.
Another reason the selected dates may not get saved are due to the formatting of date fields in the UI and this again can cause a mismatch between the db field type and value being sent to insert/update. The form values being sent to the server can be checked in the dev console by typing dmx.app.data + form id.