Date Picker jump out of the Tab order of a form

When filling a form online, after having selected a date in the "Date Picker" usually the visitor is using the Tab button to easily jump to the next field (like he do for navigating through all the others fields, from the beginning of the form up to the date picker and further).

However this doesn't work because after picking the date the cursor is not automatically kept in the date field of the "Date Picker" but instead it is lost somewhere.