If the driver in the power module computer is ok (which it should be since you replaced it), and your wiring is ok (tested connections?), maybe the fuel injector resistance is marginal and when it goes into a closed loop mode it shuts down. I think you can measure the fuel injector resistance and compare it against a tolerance to see if it out of range. (I am not sure of the value. Maybe its in the 85 factory service manual. Or if you have a new injector you can compare resitance. I read somewhere its 0.9 to 1.2 ohms cold depending on the year.)
Did you clean the contacts at the interface to the injector? High resistance anywhere along the path might cause the problem if the injector is ok.
Also, next time it does not start, try turning the key to on for a second or two, then off, then on for another second or two, then off, then on again and then crank. (Don't crank on the first two turn-ons.) This will have the affect of increasing the inital prime.
Also, check that all your fuel hoses are in good condition.