It is not possible to set managed surveys as valid only for a certain period.
After a survey is sent to end users, they will be able to respond it. Changing the Managed Survey Status to "Survey Period Closed" does not imply that end users cannot submit a survey. What it does is disable a survey in terms of stop sending a survey out.
If you are trying to use the managed survey as given in Service Desk you can notice that there are couple of Managed Survey Status like Survey Period Open, Survey Period Close. It is not possible to find any Date setting in this. It is not possible to mention a particular period of date that this survey should be active.