Hi Jyothi,
I dont see your code behind here but I can figure out that the button click is closing the modelpopup.
So, in the button click event, set the below code and check it.
ModalPopupExtender.Show();
Now, you can set the label's text property with the required value (either error msg or success msg).
Let me know if this helped you or not.!
Happy Coding.!
Thank you,
Vamsi