1000 Day "Anniversary"
The Urban Dictionary lists an obvious choice: kiloversary, also known as k-day.
(Coming soon to a Hallmark card near you.)
I would use 1,000 day commemoration to celebrate something that is not in years.
In Italian it is "millesimo giorno".
http://dizionari.corriere.it/dizionario_italiano/M/millesimo.shtml
It should be "thousandth day".
"That tradition is celebrating its thousandth day"
http://www.thefreedictionary.com/thousandth