If that task is mandatory and necessary to keep going on the project you should create another due date for that task. Also ask for help to finish that task before time is over.
Next time take this experience into account before estimating a date for a milestone.
I'm assuming that you have a manager, when those things happen here we explain the reasons and delay a little the milestone, you certainly have good reasons.
In my company we usually try to set-up a milestone based on the time that the tasks will take and also the time that we might need for other things (like bugs, little adjustments for marketing, etc).
Emil Moe
Senior Data Engineer