Car Dies Out

You're having an electrical system failure. It could be in the ignition switch or you could have a broken power wire or failed battery cable. No way to know without seeing the car for myself. Sounds like a safety issue so get it checked by an electrical shop, or an Infiniti or Nissan expert ASAP. That you've replaced the battery and alternator four times tells me that you throw parts at a car to fix it and don't diagnose anything first. Always diagnose before attempting repairs. It also tells me that you need to make friends with an Infiniti specialist or you will be victim of unnecessary, expensive problems with this car. If you want to find a specialist, here's a directory link for you: https://repairpal.com/infiniti-repair-in-norwalk-california