If the current flow holds up into the next year then Dublin will be over. Also, with some years of delay, Schengen will be over too. But that will require further catastrophes (no short supply of those).

Factors that play into it: A heterogenous asylum system of member states and a desire to push the folks somewhere else once capacities are deemed maxed out. The asylum issue is seen as exacerbating the immigration issue that is already a causing a lot of political stink (side effect: this could push the UK towards a Brexit). A raft of new legislation is being prepared in a number of EU countries as we speak. The dominoes have been falling for some time, starting with Switzerland and the UK, eventually leading to some minor version of Fortress Europe. E.g. if the Hungarian government can't use Austria/Germany as a refugee sink then it will replace the three stacks of barbed wire with a real fence.

An anthropo-political factor: In a massive crisis the first phases are marked by helpfulness and even a certain euphoria. Once the daily grind settles in and the crisis shows no signs of abating, people start getting more annoyed. Then comes the real political crunch time.

_{Schengen is toast!}