As I've been saying, with a bank run:
Corporate clients have pulled deposits from lenders including the country’s biggest, Bank of Ireland Plc.
With its lenders frozen out of Europe’s money markets and with their deposits shrinking, the Irish government may be forced to seek the bailout ministers have so far resisted.
The EU is pressuring Ireland to accept a bailout and Ireland does not (yet) want it; this should give pause to those who think that "no bailout" policies are time consistent. More generally, the simplest model is that the EU could take care of Ireland and Greece fairly easily, but the spectre of Spanish default lurks in the background. Spain is a much larger economy and the Germans cannot simply pay up to save it. All pronouncements and policies about Ireland (or for that matter Portugal) should be viewed in light of this larger "game." If Spain were fixed essentially the trouble could be paid off to go away, for now at least. But Spain is not fixed.
The longer-run question is why there should be any Irish or Greek banks at all.