Has it ever happened that just days before the big release date, you get a new set of scripts to deploy in production? But it’s just a small change the developers say!
Caramba! How are you going to verify those scripts and assure that the deploy goes well in such little time. How will you try out the forward and rollback procedures and verify that they work as intended? Will the script fail?
Set a deadline and deny updates after that date. When given the reason why you can’t update the database after your deadline, they usually understand.
Your job is to verify those changes against maybe production copy data and there won’t be enough time to download that terabyte database from your offshore site on the kilo bit bandwidth.
I would recommend at least one to two weeks to give as a deadline before the release. That will give you enough time to verify changes, try them out and even manage your ordinary work as a DBA, unless someone drops by again with new updates ;-)
Be flexible but don’t bend
Sometimes it can be okay to deploy changes, just handed over to you minutes ago, but try to avoid that. You will see that the quality of your work will improve ten folds.