Check your voltage on your battery with the engine off. Next time it does the thing, check the voltage at the battery. Regular fully charged battery voltage with engine off should be about 12.6 volts with no load.
I doubt the issue is the alt. You can test the alt by checking the voltage with the engine running. You should see 13.7 to 14.7 volts with the engine running.
I don't suspect the battery, but do the tests to rule it out.
Check and clean the connections to the battery.
Follow the smaller wire off the positive post to the radiatorsupport terminal and check and clean that connection. This wire runs across the radiator to the horn relay bussbar. Check and clean the wires and screws on the bussbar below the horn relay. You may find a fusible link between the battery positive post and the radiator support terminal. Check it and see if the wires feel mushy.
When the car fails to start, check for power at the horn relay bussbar. If there is none there, the issue is between the horn relay and the battery connection of the smaller wire on the positive post.
From the buss bar, there is a black wire with a fusible link then the wire turns to red in color. If you have power at the bussbar but the car wont start and you have no power to anything in the car, this fusible link is probably the issue. Sometimes you can see the wires at one end of the fusible link are burned or mushy. Sometimes the only way to tell if the link is bad is by testing for power at the circuit. But, it may pass voltage until you put a load on it.
Sometimes when you put a high load on a poor connection or bad fusible link, the connection will fail. Wait a minute and the next try it might make the connection. Complete failure will eventually occur.
Bottom of horn relay. The bussbar is just a piece of metal the creates the circuit between the red wire coming in from the 4 way splice that leads to the battery. It also a place for other circuits to get battery power.
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This is the bulkhead terminal, I called it the radiator support terminal because it's on the radiator support just in front of the battery.
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