I was alerted to this interesting facility by this old post from @baboon According to this article from 2016 they still hold Saiga, and the 'zoo' covers an incredible 180,000 hectares. The big question is is this facility open to the public? I will be in the area early next year so will definitely try for a visit.
Oops! China protection center prepares endangered animals for Spring Festival - Xinhua | English.news.cn
A little further info: It appears that part of the facility is open to the public, operating under the name of Shenzhou Wildlife Park. The big question of course is are any saiga onshow there. Nearby is something else called the 'Desert Park'. It's unclear if this is a public park or a private theme park, or whether it is linked to the Animal Protection Centre.
You can try to communicate them before your travel (0935-2516381 is their number shown on the travel websites), and see if there are any chances to go to the off-exhibit area......