If I've truly painted myself into a corner in a situation like this I'll sometimes break character to let the party know that the NPC is suffering from "cutsceneitis" and offer them a get-out-of-death-free token they can redeem later if they'll let this current guy go as planned.

Generally speaking it's better to roll with it if at all possible, though. You can perhaps Final Destination the guy and have him be a bad luck magnet for the party until he's taken care of. Or just throw out your plans and see where this new adventure is going to go. I still regret not doing that a few years back when there was a sole survivor of a battle whose only purpose was to spout a few lines of information and then conveniently die, and the party tried to save him. If they'd succeeded I now realize in hindsight it would have been a lot of fun, the party would likely have wanted to kill him themselves in the end.