Hi,
Thanks for using Syncfusion Products.
"this.Datetimepicker.Hide()" is nothing but control.Hide(). So once you hide the control you could not show the popup of Datetimepicker.
Here is the simple sample which illustrates to hide the popup programmatically.
http://www.syncfusion.com/uploads/redirect.aspx?&team=support&file=WindowsFormsApplication1526030679.zipPlease let me know if you need further assistance on this.
Thanks,
Karikalan