My 1981 CJ seems to run perfectly, and in the last 5-6 times I have driven it 3 times it will run great, then it will just dies. Before I have always been able to start after 1-4 times trying, but this last time I ran the battery down and had to push it. Where should I start trying to figure out the cause of this.
These sudden and erratic failures are difficult to pinpoint. However there are some basic tests you can do when it stops.
take off the air cleaner and work the accelerator, you should get a good spurt of fuel. If you have an electric fuel pump it could be an electrical or pump failure. If mechanical this is less likely but check you have fuel at the carb.
The other likely culprit is the ignition. You do not say what setup you have so I assume it is a Duraspark ignition module.
You need to isolate where the problem lies. It may start right up again so this may take some time to track down.
First thing is to get a test light (not the LED kind) and take the leads off the coil to test whether you have voltage and signal. The red with tracer wire should have 7V in Run and 12V in Start, a dim and a bright bulb when you connect to it and the -ve battery terminal.
The green wire should be connected to one end of the test light, other end to the battery +ve. the lamp should blink as you crank the engine.
If all athat works and there is no obvious flaw in the wiring you need to test the coil and distributor. Get an old spark plug and connect it to #1 spark plug lead and rest it on the cylinder head. As you crank you should get a bright blue spark and a good crack.
I suspect you will find it is an intermittent fault in the ignition. I had a short at the connector plug to the ICM, test procedure isolated it pretty quickly.
Once you have it isolated look up Jeephammer's old posts and there are more detailed tests that you can do.
Some good advice on here, and BagusJeeps troubleshooting tips are fantastic. His post is definitely the correct way to go about diagnosing your issue. I'm a gambler and have been ridiculously lucky when I foolishly throw parts at my Jeeps. Check for spark at the coil. Odds are it's the ignition module, or, on rarer occassions, the ignition switch under the steering column.
These modules fail way to often, I went with an MSD 6, more reliable, more power, better etc etc etc.
Put the coffee/beer down:
A friend found on his 'stang he could pee on the ignition module and it would cool enuf to run again, one night, drunk on his as* he forgot to turn off the ignition, when it cooled enuf to work again, well he changed it next day! Shocking,,,