1999 Durango 4wd SLT Problems

I have a 1999 Durango that is going dead when I stop at stop lights or stop signs. This has happened several times and then it will start back fine.
Last night I went through a drive thru and it went dead and would not start back. I let it sit overnight and it started fine this morning. I have checked the fuel pump, battery and alternator. Does anyone know what might be the problem?
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