During a press conference of China’s Taiwan Affairs Office on 25 June 2016, spokesman An Fengshan said cross-strait contact mechanisms had been suspended starting from May 20 [the date of President Tsai’s inauguration], due to Taiwan’s inability to confirm the “1992 Consensus”.
Relationship between Taiwan and China are not handled by the two sides’ respective foreign ministries, as China considers matters related Taiwan as domestic affairs (as they try so very hard to remind the world every time other countries say or do something related to Taiwan), and Taiwan’s current constitution has yet to be modified to allow its government to consider mainland China as a separate country. Instead, China, under its State Council, has a Taiwan Affairs Office 國務院臺灣事務辦公室, while Taiwan, under its Executive Yuan, has a Mainland Affairs Council 行政院大陸委員會. However, even though both ministry-level offices have been established since 1991, official meetings between the two ministers did not happen until February 2014.
You see, China does not want any effort to appear like it recognizes Taiwan’s government as legitimate, which it fears communications between two government bodies would do. Thus, in 1990, before the official establishment of the offices on both sides, China also established the Association for Relations Across the Taiwan Straits 海峽兩岸關係協會, while Taiwan established the Straits Exchange Foundation 財團法人海峽交流基金會, both semi-official NGOs, to serve as liaison bodies between the two sides. ARATS and SEF also handles several matters similar to what an embassy would be able to in a foreign country.
Chairmen of ARATS and SEF first met in Singapore in 1993 and subsequently in 1994 and 1998. Contact was broken during 2000-2008, as China refused to deal with Chen Shui-bian’s DPP government, and re-started in 2008 after Ma Ying-jeou of KMT was elected president. Today we are seeing China has once again refuse to deal with Tsai Ing-wen’s DPP government by cutting off contacts between Taiwan Affairs Office and Mainland Affairs Council, and potentially between ARATS and SEF. It’s almost as if they hope the problem would just go away if they bury their head in the sand like an ostrich.