You have the option to keep your event registration open, or limit it to a number of days. This option is set in the Template and does not need to be changed for every event that you schedule.
Edit Template
Head over to your templates and click "Edit Title & Detail"
You have an option that says, "Keep Enrollment Open". If active (slider is to the right and bright blue), your enrollment is open and will never close. However if you turn this off, you have the option of entering a number. This will be the number of days to keep the enrollment open AFTER the event starts. For instance, if you enter 2, and then schedule an event that starts on March 1st, registration for this event will close on March 3rd, 2 days after the event started.