Ignition experts needed

Well. Since the entire ignition is brand new, I decided to at least replace the starter relay, to fix that issue. A-zone had 1 on the shelf. Came home wired it in and fired up the car. Waitinig for it to die again, I noticed the guage was pretty steady this time. 45 minutes I sat in that thing, revving...idling...revving. Couldn't try driving it due to weather, but it didn't die. Hasn't run that long since before this issue.
I can't believe a starter relay could fix it though, since I had the ignition wired right to the battery.
The battery is only 2 years old. I did notice that when I finally shut 'er down, my voltage regulator was really hot. Almost too hot too touch. Doesn't seem right. Maybe like A340 said, I have a bad battery...or regulator. Accel tells me a big voltage drop OR spike will shut the box down, temporarily.
Can a bad tach wire really short out the coil? I've notice that since this problem began my shift light on the tach is very faintly glowing, when the car's running. Just noticed it tonite in the dark garage.

I'm really reachin', I know. Think I might replace the voltage regulator tomorrow.