After a quick reread of the OP's post, it's very obvious (to me) that the problem is not enough power bars in WEPS... Power Bars not to be confused with PIPS...
If weapons recharge is low then rails guns will be showning as overheated and so will not even fire until there is enough power in weaps to fire them, if you have a multicannon too, that will fire when 1 bar gets recharges, so if you are holding down BOTH weapons or they are on the same fire group THEN your rails will seem to fire very intermittently and then the cannons will stop as well when you empty your capacitor bank...
I have the same problem on my cobra when I am firing both beams and pulse lasers continueously on a target and the capacitor drains, it will fire whichever one it wants to at the time, sometimes both pulse and sometimes one or both beams briefly but only if the pulses do not have a lock and the beams do
If you have not already, upgrade your power distributor to the highest you can, for maximum capacitor resevere
if you already have the best one for the ship A(whatever the max size of the slot is) then you need to plan your combat and power use differently... to ensure you can fire your rails when you want to etc... That might mean making time during combat for weps capacitor to recharge etc