I'm a bit surprised that the divorce rate has been holding steady for the last 5 years, although I'm always suspect of any government stat, seeing as how they often have their own spin.
It occurs to me that any of the larger and more cosmopolitan Chinese cities should be showing increases in the divorce rate, not just Beijing. I'd say that the increasing divorce rates are a reflection of the changes in Chinese society; until fairly recently, divorce was a stigmatizing word and concept, and couples would stay married in name if not in deed in order to avoid the "D" word. A divorced male was often limited in his job advancement prospects if divorced, and a woman, especially with a child, had low expectations of remarriage. My nine-year Chinese girlfriend was married but separated. Her husband had asked her not to go through with a divorce, as he was worried about the effects of a divorce on his career and how it would look to his parents. She obliged and I didn't mind.
However, the younger generation and urban couples in general are developing a different attitude regarding divorce and are far more likely to get divorced if they decide that they made a mistake. My current Chinese partner is married as well, but this past May, she decided that she would ask her husband, with whom she no longer lives, for a divorce. She was worried about what her parents and friends would say, but decided that her own happiness came first. She still was influenced to some degree by the old attitudes, but as part of the 'new generation' of young married Chinese, ultimately made the decision to go through with the divorce.
I suppose you might say that this is just another case of Western influence on Chinese society, or perhaps it's just part of the 'new China' that is part of the evolution of society that most nations go through eventually. Yes, "social media" may make it easier to cheat on your spouse, but cheating generally comes after unhappiness in the marriage, so I don't think that modern social media is as great an influence on the rising divorce rates as many people assume it is. It's just a different way to cheat.