Sounds like heat soak issue. You have a chance to find this with a scope or nice scan tool and some live data drive cycle testing. It could be any number of things causing it.

 

I realize this is both a) throwing parts at the problem and b) a complete apples to oranges comparison, however my 1993 Jeep 4.0 ZJ began acting in a very similar fashion when the OEM crank sensor began going out after ~220K miles. The car would run fine for about 1-2 hours then would shut off at highway speeds (never at idle). Sometimes it would restart immediately with the turn of the key, but other times I would have to wait 5-10 minutes for it to get it's act together enough for me to restart it. Then it would run for another 15-20 minutes, before shutting down again, and me having to repeat the whole thing.

Crank sensors aren't too terribly expensive for this vehicle (the H3), so you could always buy one, throw it in, and see if that fixes the problem. It's not too terribly difficult on the 3.7 either.

Okay, I'll quit bringing up Jeeps on this forum.

 

You need to scan it with a decent scanner (not a cheap code reader) and post up any stored/historical codes.

Does it have any aftermarket remote starter or alarm on it?

It could be fuel, crank timing, or even ignition problems.

 

^X2 SCAN & POST THE CODES!

Sensors that frequently cause engine stalling include the crankshaft/camshaft position sensors (timing issues), mass airflow (MAF) sensor (incorrect air-fuel ratio), and throttle position sensor (TPS). Other culprits include the oxygen () sensor, coolant temperature sensor, manifold absolute pressure (MAP) sensor, and a faulty idle air control (IAC) valve.

Key Sensors and Their Effects:

• Crankshaft/Camshaft Position Sensors: Crucial for timing; failure causes unexpected stalling and starting issues.
• Mass Air Flow (MAF) Sensor: Measures air intake. Dirty or broken MAF sensors confuse the ECU, leading to improper fuel mixture and stalling.
• Throttle Position Sensor (TPS): Tells the car how hard you are accelerating. A bad signal causes hesitation and stalling.
• Oxygen () Sensor: Affects air-fuel ratio, potentially causing rough idle or stalling.
• Engine Coolant Temperature Sensor: Can cause the engine to stall due to incorrect fuel mixture, or actuate a stall to prevent overheating.

Stalling often happens while driving or when coming to a stop, frequently accompanied by a check engine light, rough idle, and poor acceleration.

 

I read an online search that mentioned the batter terminals like Doc mentioned and the Crankshaft Position Sensor like 008 said.

The H3 has not thrown a CEL. Nor does it have any stored or pending codes in the computer.

The sensor is not expensive, and the crankshaft and camshaft sensors were on the to change list when the cylinder head is replaced.

The H3 is stock with no additional features added.

Thank you for the suggestions, and will update when the sensor is replaced.

 

My scanner is only a read and delete code type.

To do the learn procedure of the Crankshaft Position Sensor, which Scanner would you members recommend for a weekend type mechanic?

 

The Scan Tool that I used is the VIDENT iLink400 which so far has been 5/5, and would highly recommend. It's only around $150 bucks on Ebay but it has an incredible amount of functionality. I bought one out of sheer curiosity and I do not regret it one bit. You can do CPS Relearns, and even re-program your lock/unlock remotes if needed (and that is just scratching the surface of it's functionality).

Avoid any of the Scan Tools at Harbor Freight that have the System Tests/GM Functionality, not because they are bad, but because they are too new for the H3. I purchased one about a year ago to do a CPS relearn and it was not compatible with my 2007 I-5. Fortunately Harbor Freight did not charge me a return fee after I tested it in their parking lot, and determined that (other than the Generic OBD-II data) it was not compatible with my vehicle.

That said, a Crankshaft Relearn is not required to simply get the vehicle running; that is, you can install a new sensor, not relearn it, and the engine should run perfectly fine with no CEL codes (should being the key word). The CPS Relearn is really to fine tune the system. If you install a new sensor, and the car continues to die on you, doing a re-learn will not help with that.