In early September, Mario Draghi and the European Central Bank announced a grand plan to come to the aid of euro-zone governments facing unworkably high borrowing costs — countries like Spain and Italy. It seemed like a reasonable enough plan, despite all the potential hitches, and the euro crisis quickly faded from the headlines. Well done.

You can't hide from the doom, Bankia! (Associated Press)

But before anyone breathes easy, it's worth taking a look at this new investigation from Bloomberg's Yalman Onaran. As the story details, there's still a massive bank run going on in the euro zone that's threatening to tear the currency union apart. Over the past 12 months, some $425 billion in deposits have been pulled from banks in Greece, Italy, Portugal and Spain. And about $390 billion in deposits have piled up in core euro countries, particularly France and Germany.

That might sound like a mundane bit of accounting. But it's potentially quite dire. And this slow bank run is a major reason why the crisis in the euro zone isn't likely to go away just yet.

First, a rundown of why these deposits are shifting about in the first place. Imagine that you have tens of thousands of dollars stashed in a bank account in Greece. You keep reading Wonkblog and hearing that your country might get kicked out of the euro — in which case Greece would go back to using drachmas for currency. If that happened, your bank would forcibly convert all your saved euros to less-valuable drachmas, and you'd have a harder time affording imported goods or traveling abroad. That sounds unpleasant. So, one sensible thing to do is put all your euros in a German bank, for safekeeping.

As Bloomberg details, people have been doing this all across the euro zone on a breathtaking scale. Depositors in Spain, Italy, Portugal and Greece are all sending their money abroad. And this has all sorts of economic consequences.

For one, banks in these "periphery" countries now have to offer higher interest rates to entice depositors and get money. Some Greek banks now pay as much as 5 percent interest on their deposits. In turn, this means that Greek and Spanish banks have to charge higher interest rates on the money they lend. Businesses are paying more to borrow money. Those higher rates stifle economic activity and make it harder for countries like Spain and Italy to grow. Some banks in Spain, for instance, now face the risk of losing money on every mortgage they issue — which makes it tough for Spain's shattered housing market to recover.

The International Monetary Fund has warned that such financial "fragmentation" could undermine the euro zone. The countries with the biggest debt problems — Greece, Portugal, Spain, Italy — are now having trouble revving up their economies because of the drain on their banks. The European Central Bank has tried to swoop in and provide cheap loans to the troubled banks through its long-term refinancing operations, but that hasn't stopped the fragmentation.

So that brings us to the most recent plan by Mario Draghi of the European Central Bank to save the euro. Draghi, remember, promised to use the ECB's unlimited firepower to lower the bond yields (borrowing costs) for troubled nations, albeit with conditions. The hope is that this gives the governments of Spain and Italy time and space to whittle down their deficits. But Draghi's plan arguably won't fix the fragmented banking system, which is suppressing growth in the euro zone. And without growth, Europe's debt crisis won't go away.

Does anyone have any better ideas? Perhaps. One proposal is for the euro zone to set up an integrated banking system — with euro zone-wide deposit insurance. That's what the United States has. No one with a modest-sized bank account in Florida needs to worry about his or her deposit vanishing, because it's guaranteed by the Federal Deposit Insurance Corporation. The euro zone doesn't quite have anything like that. (Greek banks are insured by the Greek government, which.... yeah.)

And yet, as Delusional Economics reports Thursday, European leaders are still very, very far from agreeing on how to integrate their banking system. At this point, they're still arguing over how to supervise banks. Germany is still rejecting deposit insurance altogether. That suggests that the slow-moving bank run may well continue — and the odds are good that the euro crisis will pop back into the headlines sooner or later.

Related: German court approves a plan to save Europe. But is it a good plan?