I haven't seen that problem. Most of the time I get the first shot off. I have had glitches where it seems as though my weapons stop firing after I take damage.
This seems to me to be engine lag and I experiece it quite a bit. Expecialy when torpedoes are "blowing up", launched either by my ship or the others (NPCs or player ships seem to make no difference). It seems they have the engine doing more than it can keep up with. This engine lag is pretty much in everything but Cryptic has masked this decently in space combat however ground it shows up alot.
You have to look for it in space. Dstahl made comments on this engine lag in the S-4 revamp. He was able to "speed" some things up in the ground portion but the lag is still there and probably always will be.
I was getting actualy used to it until I beta-ed another game that used the Hero engine and the difference is really appearent between that and the Cryptic engine.