I think that this is primarily a storytelling question. The answer why any antagonist is a danger is due to the circumstances that the heroes (or in this case, PCs) are allowed to interact with them. Only introduce a blatantly antagonistic character you want to have stick around when the PCs are incapable of dealing with that threat. Have the dragon meet your gunlugger when she's been captured and is at the dragon's mercy. Or have the dragon have some form of information that the gunlugger needs, so killing her would be a decidedly bad idea. Hell, have the dragon try to recruit him! Why not?
Certainly custom moves are important as well. Give her the inverse of a playbook move, stuff that keeps her living. The Faceless is great for this. Take a look at Pit bull:
Whenever you take a debility, name the person you hold most responsible.
Take +1 ongoing to all rolls versus them, forever.
This is a move designed to make the faceless want to take debilities, by giving him a benefit for doing so. How can we manipulate this to work for our purposes?
How about:
I Can Make it Worth Your While...
Whenever (insert dragon's name here) would die, the killer has the option to instead take +1 ongoing for all Hard, Cool, Hot, or Sharp rolls versus them, forever.
This move gives an enormous incentive for players to keep this character alive. You get to knock this guy about over and over and over again. To be fair, this move facilitates the character becoming weaker over time, but that might be what you want! It sort of reminds me of what Bowser has become in Mario games. He's just less and less of a threat.
There's likely a more elegant move that could work properly, but I think that your best bet is either to only show the dragon when the PCs can't kill him (not that fair, and against the principles if you do it more than once, probably) or create some custom moves or relationships that are less of a barrier for the players, but instead incentivizes them to keep the dragon alive. That seems more interesting to me, personally. Also, don't get too attached to NPCs, like, ever. Because we shall all perish in flames.
Hope my ramblings are of some use! I think the scenario you described was pretty funny, however. Reminded me of the famous sword fighting scene from Raiders of the Lost Ark.