Uber's policy is that the car has to be 10 years older or newer. Their website says 2008 or newer (10 years).
My understanding from what someone at the green light hub told me is that you're given between 3 weeks to 6 months before you are told to get another car, however the way they worded the situation to me let's me know that they themselves aren't sure when a car becomes ineligible until it happens.
I'd assume the message would be sent somewhere between February and June. I highly doubt they'll let you use it until 12/31/2018 considering that NYE is their busiest night. They technically would have to allow you to use the car until 01/02/2019 to avoid disruption on NYE going into NYD (thinking logically). Of course, logic is something Uber lacks.
If it makes you feel any better, wait until your registration has to be renewed for them to tell you it's ineligible. I'd assume that would trigger the "ineligible vehicle" prompt when they validate the new uploaded registration.
Someone with experience to this would best answer the question.