What does anyone keep his or her money, in any sizable amount, in an Irish bank when you can have a euro-denominated account in a German or English bank? Admittedly the interest rate on Irish deposits may be higher, but that has to be matched by a comparable rate of return on bank assets, which right now doesn't seem possible for Ireland. (One fear I have is simply that it isn't and that Irish banks are falling more deeply under.) No matter what bailout is promised, at the end of the day your "euro" might no longer be a true euro.
Yet once deposits flee Irish banks in large enough numbers, the Irish government has to suspend convertibility into the euro or in other words restrict capital movements, whether that is legal or not under EU law. And then suddenly Ireland has a new currency, whether they admit it or not.
There is also a contagion effect. Let's say that Portugal, Spain, Ireland, and Greece are the weak members of the eurozone. A pending bank run in any one of these countries could trigger a convertibility suspension in the others.
Do you think that all of these countries have a strong enough (or maybe I should say "weak enough"?) political economy to impose ongoing cuts in living standards on their voters, to pay back their debts in full? These countries not only have to do the hard work behind the payback, but they have to convince investors and depositors in advance that they will follow through consistently.
That's why I don't think the current configuration of the eurozone will last. A collapse would require only one weak link in the chain.
Right now I would not keep my money in any Irish bank, but presumably some of the people in Ireland remain loyal to their institutions. It's odd how the eurozone is premised on a cosmopolitan Europe, but right now it is hanging by the thread of some very provincial preferences.