The most likely reason for this is that you have set a Maximum responses number.
A survey will automatically close when it has reached its maximum responses. You cannot re-open a survey that has reached its maximum responses unless you change or remove the maximum responses number.
The Maximum responses number is found in the survey’s 
Distribution settings, under Survey responses. You can change or remove this number at any time. Once you have done this, you will be able to extend your survey’s closing date and allow it to receive more responses.
