You can control for how long each survey is available on the mobile app. This is called the "survey availability window".
On the My Surveys page of the account you are editing press the gear icon, labelled "Momentary Survey Parameters". More information is in this article on User Settings. This opens a window that allows you to define the start and end point of the survey availability window for each schedule type.
For each schedule type use the drop down menus to define when, in relation to the alert, the window should open. It can be open before the alert goes off. Then define at what point after the alert it should close.