Can't find any vicious cycle leading to an unstoppable weakening of the Euro when I thought through and create this NaviMap. If the European leaders are utterly incompetent, perhaps we will see the Euro finished. They may not be first class leaders but not completely hopeless (box 2).
We all know Greece catalysed this crisis for them (box 1) and a few more countries lumped together as the PIIGS countries are at stake because of their extreme indebtedness and their doubtful ability to service it. Box 1 and Box 2 caused large numbers of investors to lose confidence int he Euro (box 3). The Euro falls (box 4). At the "right price" remnant believers remain to shore up the value of the currency (box 5). Depending on Box 2 and may be over the medium term Box 1, the value of the Euro is decided.
Box 1 can lead to Box 6 which is the agent for contagion across the Atlantic.
Conclusion: Hard to see the Euro in free fall because there are no vicious cycles.