We previously used a program called Volunteer Scheduler Pro and we could choose for volunteers to not be able to remove themselves less than 48-72 hours in advance. And when people did remove themselves, it would send an alert out to all volunteers that have the qualifications needed to get the spot filled. So If there could be an automation feature along with it, it would make it easier on our staff to get the spots filled.
You would also need to have the setting for each organization to decide the time frame that suits their needs.