You can set an RSVP deadline in your Event Settings under the RSVPs tab. This will prevent your guests from RSVPing past a certain date. This feature is currently only available in the Partiful app.
To add an RSVP deadline, open your Event Settings by clicking Edit and then Settings on your event page. Then click on the RSVP Options tab.
Click on "Accept RSVPs" and then open RSVP Deadline. From there, you can use the calendar to set the date and time by which you'd like to close RSVPs!