CB Invites does not have an expiration feature. It's a good idea though and was added to a few other plugins already. Have added a feature ticket for this.
forge.joomlapolis.com/issues/8381
I cannot advise you on core modifications to CB Invites as we do not support core modifications. Once implemented you'll be able to select from a parameter how long the invites remain active (e.g. 1 week from send date).
I do not have any suggestions on how to implement this even with CB Auto Actions. While there are triggers for acting on there's a lot involved with expiration behavior and would likely take 3-4 auto actions with custom coding.