What's your weapons energy level at? You might be firing too many and reducing your weapons energy to 0 midway, so only some can fire.
110 weapon power with 5+ total EPS flow regulation. Same issue. I hit spacebar, four weapons fire, the other, still plainly highlighted in white indicating it can be fired, doesn't, until I press spacebar again.
Hmm not seen this personally, but then I've got my 5 beams + 1 dual beam on my Sovereign all set on auto-fire. Took alot of frantic right clicking to set it up, but with practice it wasn't too hard in the end.
So one hit of space bar and off they go - 3 forward firing, to 5 broadside beams. Torps are on manual fire.