Logic triggered weapons only activate once, and can't activate again. Confirmed with beam, cannon, and salvage, salvage+beam for sure.
Assigning the weapon to a logic block (eg, a button) also removes the computer from the ship's weapons menu. That may be intentional. But removing the logic block doesn't bring the weapon back into the menu until the player restarts the world, which certainly isn't intentional.
Screenshots: https://imgur.com/a/A9C2b