It certainly seems like the circumstances under which the UN Convention on Refugees was written no longer reflect the realities of the world. Increasingly, refugees are fleeing natural disasters and near-collapse of governments instead of genocide. Whereas once you were fleeing certain death, it seems like now it may be damaging countries by removing the very people who would help rebuild or restore order. They also seem to be using the system for economic migration instead of actual asylum.

There is also a large unintended incentive to enter a country illegally and then make an asylum claim, since it is faster and often means near-immediate access to state benefits. Article 31 of the Convention [1] is the one which grants amnesty to asylum claimants entering illegally and it made a lot of sense post-WW2, but seems like it's going to seriously test some country's ability to maintain order in the face of potentially tens of thousands arriving overnight at a border.

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[1] http://www.unhcr.org/3b66c2aa10 on page 29