We will arrive at Xi'an Airport on August 4th,2016 at 11:30 PM . Does taxi run late (midnight)?

Yes, you can still find several taxis outside the airport. Don't worry. If you wanna take a cab from the airport to your hotel, it may cost around CNY 130 at night.
Or upon landing, you can take shuttle bus Xishaomen Line and get to Xishaomen Airport Business Hotel. The operating hours of this bus line will until the last flight arrivial. So you can catch it. The duration is about 60 mins with the fare of CNY 25/person. After that, take a cab to the destination. The cab fare would be around CNY 20.