I've had this same problem. And yes, I've fire tens of thousands of missiles, I'm familiar with the process. The error happened during just one fight so far, 5. 42, with one set of ships.
Note: This problem happened on the Battle Control screen (F8?) workaround was to go to the Individual Ships and manually fire each ship, one at a time. Fortunately a small battle, so this was feasible.
Missiles on ship, check.
Missiles loaded in launchers, check.
Launchers assigned to fire control, check.
ECCM assigned to fire control, check.
Target assigned, check.
Target in range (FC has range of 35m, targets at range 10m. and it only has ECM-4, so yep, in range). Check.
Click the button to have all ships fire, and the launchers are no longer assigned to the fire control. "Assigned Missiles/Buoys without Shipboard Fire Control" is now all of them.
Reassign launchers to the fire control (only one on the ship), verify everything else is still set, click button to fire the launchers assigned to the selected fire control, and the launchers are now unassigned.
Reassign launchers, try again, same results. Try the next ship, same problem, try a third ship in the task group, same problem. Shut down Aurora, reopen, verify everything, same problem.
Go to the Individual ships window, combat tab, set everything up again just to be sure, fire, go to the next ship, repeat 19 times (gunboats, they run in packs).
And the missiles fire.
Combats prior and after that one, worked as expected. No clue.