Is this article updated?
We are working on AEM 6.4.4.
We also have similar workflow, in one the steps of workflow a participant has to choose activate later and he need to choose date/time from datetime picker.
But the moment we enter anything using datepicker, the date/time values go away and also the datepicker.
In 6.4.3 it used to work, on debugging more I observed that, there is some difference in
/libs/cq/inbox/gui/components/inbox/clientlibs/commons.js between SP-4 and SP-3 for AEM 6.4.

Below is the code from 6.4.4:
dialog.off('coral-overlay:close' + workitemActionDialogNS)
.on('coral-overlay:close' + workitemActionDialogNS, function() {
// remove the injected dialog pieces...
$(".cq-inbox-dialog-injection-anchor").empty();
});
Above highlighted line is removing the entire widget from dialog.
Till SP-3 it was working, please suggest. Thanks in advance.