They'll have to negotiate trade statuses, which will invariably be more favorable to the EU than to Britain. See the case with Norway and Switzerland, though possibly even more uneven owing to the fact those two nations were established as non-EU early on, before the EU was a powerhouse. And not just trade status (that's just the most immediate, being the core principle of the union) but almost all levels of European relations will have to be sifted out. Almost all will be to Britain's disadvantage. The US is the last nation in the world that needs to pile on penalties.
As for keeping the EU together... 
It's not the United States. That is, it's not a single nation made of component states. It's 28 (well 27 now) independent nations in a tightly intertwined alliance. Each is free to go its own away if it wants, for good or ill. And eventually, most of them probably will. Not because of Brexit, but because of history. Nothing lasts forever in world history except China and Egypt - and even those are pretty dynamic. The EU is guaranteed to fall apart at some point, maybe sooner, maybe later, but guaranteed to happen eventually. It's probably better for nations ot voluntarily leave at their own decision, than for the whole thing to crumble under its own weight and drag everyone down, like it came frighteningly close to doing a few years ago.
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