If you're using a weapon that exhausts when used (like the flamethrower), and you don't kill the monster in the first round, do you keep the weapon's bonus for the following round of combat or lose it because it's exhausted? I imagine you keep the bonus until you switch hands, but I'm not sure.

You loss the bonus except if the weapon is a 357. Magnum.

MrsGamura said:

I never noticed it said "until the end of this combat." That was a weird weapon exception.

Anyway, here's the precedence from Kevin Wilson's answers to rules questions:

Type 3: (Burst) "Exhaust before making a Combat check to gain +X to that check."
Examples: Flamethrower, Carbine Rifle.

This type is used for only a single combat check, and it is then exhausted and cannot be used again until refreshed.

Is it the same then for Holy water and Dynamite? One combat check, then discard?

Yes, it's the same for these two. You don't ge to sprinkle some water or blow up the building every round