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My other response seems to have disappeared, so I'll try again.
About the only solution I can see (which isn't a great one) is to have someone else step in with some excuse to have one of them leave with him/her. The person leaving can save face by saying something like "This isn't over!!"; I'm not sure what that would be other than saying someone else needs help, your house is burning, whatever. It won't solve the underlying situation, but it will get them out of the deadlock.
I think the biggest problem is that too many people believe that every confrontation has to end with someone dying or being beaten down in some other way. Many times those conflicts can be acted out with no actual violence involved, so it doesn't matter if the other person responds as expected. If you're one of the participants, you have some control over it; if you're just an observer, you can always try to find some way to end it without having to rely on either of them being the `bigger person' and accepting defeat.
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