I'm not a wire expert but was chasing down a similar problem on my car before.
Without a constant 12 volts my ignition system would not run.
Unfortunately our cars were not blessed with great wiring to start.
Couple in decades of wear and fatigue and not to mention a backyard mechanic or two getting in the system and making changes, these systems can weaken over time.
From what I read, always make sure you have a good ground, make sure you alt is producing more than 12 volts, and begin tracking down where your voltage drop is occurring.
Possibly a junction point?
Mine was happening at the fuse box itself, with years of splicing and too much juice being pulled through too small wires.
I ultimately ended up replacing the old through a used group of wires starting all the way at the bulkhead and adding a new additional fuse box for add ons ( fans, neon, extra power point ) also leaving myself with additional extra points in case I want to run an electric fuel pump or another extra.
Hope that helps
