Car shut off while driving on the freeway then restarted?

Background: the vehicle usually took two tries to start and wouldn’t start if the gas was low (but still above E) and parked with the tank lower than the engine, i.E. Parked pointing uphill.

A few days ago, the car shut off on me on the freeway and wouldn’t restart so I got a tow from the city where I waited for my regular tow company. In that time, the vehicle started again twice but only if I waited about 15-20 minutes. The first time it shut off again while idling after around 5 minutes. I got the vehicle towed then went back to it 36 hours later with a multimeter.

Battery voltage was about 12.67 and the car fired right up. This was around 8am so it wasn’t hot...I’m wondering if it has to do with temperature. My temperature gauge is always right where it should be, between the two dots and this has never changed.

I drove about 1.5 miles to AutoZone, parked and checked the battery again. Still the same. Then I tried to restart the car right away. Nothing. I waited about 20 minutes then it started and I checked the battery’s voltage while revving the engine at 2,500 RPMs = 14.17v.

I did it again with the lights on = 14.7V

Again, with lights and 2,500 RPMs = 14.16v.

Both off = 14.27v.

An employee checked the battery and alternator after I turned the car off and tried to restart it unsuccessfully. The machine said the battery was good, but the alternator was bad. It didn’t make sense because the battery always checked out.

I waited. We tried again later, and it wouldn’t start but then the machine said the battery was bad. Hmmm.

I pulled the battery, popped the caps, noticed the fluid was low, added distilled water and put it on a trickle charger. It charged up to 12.71v. Great!

This morning I put the charged battery in, and the vehicle fired right up on the first try, strong and solidly. An improvement. Turned it off. Fired right back up. Again, same thing. This is before I started driving it at all.

I was able to move the car and park it (drove about a 1/4 mile). Then, hours later moved it and was idling with the A/C on for about 10-15 minutes, then it turned off. Ugh. Why?

Another 15 minutes or so and it started back up but not as strong.

The vehicle never feels like it’s struggling for adequate fuel supply. Please help.