Could be the solenoid going out. If that is going bad then it might work and then have a loose connection coming undone. I think my dad bought a rebuilt kit or new one for ours for less than $10 at Advance Auto or Autozone. Don't know if that is the problem, but is a cheap thing to try before going all out for a starter.

Chris

 

Is the solenoid located on the starter?

 

Sounds like a combination of problems to me.
1. when it's turning over the engine doesn't fire
2. After a while it will quit turning over.

It could be that the resistance is building up in the switch or wire to the ignition switch when you crank it over and over.(Very common to Jeepsters) To check that, you can use a screw driver or metal wrench or something to reach under the car and short the big battery wire terminal on the starter, to the little wire terminal that is closest to the engine block. If it starts cranking again, then you need to replace the large wire from the battery to the ignition switch. Preferably with a 10 gauge wire.
If crossing the terminals on the starter does nothing, then the starter is bad, or maybe a loose connection at the starter or battery.
I like to use a remote starter switch for this test, they are cheap at an auto parts store. Just a trigger switch with two wires and aligator clips on the ends. It replaces the screwdriver or wrench.
Your V-6 should have the delco starter which should have the solenoid on top of the starter. They switched in about late 69, but there have been some later ones that didn't.
If you follow the big positive battery cable from the battery, if it goes right to the starter, then you have a solenoid on top, if it goes to the fender to a relay/solenoid, then you have the older prestolite system. Get rid of that if you do.

Maybe once you get rid of the starter (or wire) problem, you can figure out why it is not firing. Some times fuel leaks out of the carburator bowl after a period of time (or evaporates) and you have to crank it until fuel gets back into the carb.
You can also try pouring a capful of gas down the carburator first and then crank it to see if that is what it is. Or go to the auto parts store and get a spray can of starting fluid.

 

As Tom said, could be the wire that triggers the solenoid.

And - could be a loose/defective battery cable too. Next time you try it and it stops turning - feel all along the battery cable and the terminals. If it's hot, there's too much resistance right there. Determine why and fix it. It can happen in the middle of the cable as well as the ends.

And - that includes the ground cable too. Make sure the (-) cable goes to the engine block, not to a body part. It too will get hot if it's got too much resistance.