When you use separate fields, you are setting only a part of the DateTime attribute, which means that it will go back to 1970 if you only change the time.
What you have to do is show only one datepicker input field and set the property (Properties -> General -> Date format) of it to: Date and Time. now you can enter the date and time in the same field and it will work fine.
If you really want to have two separate fields, you will have to use two different attributes. Then after save, you can merge them.
For an alternative datepicker, type 'date' in the app store search and make your choice. I like the Jquery one.