Why would a 2000 Sonata electrical system shut off for less than a second and then come back on immediately while the car is moving usually around 20 to 40 miles per hour?

Are you sure it is the electrical system that shuts off? I have a 2000 Sonata that stalls at any speed and even at idle. But it is not the electrical system as the radio continues to function. I have read that I should have a dealer look into replacing/rerouting the MAF (mass air flow) sensor-connector wiring harness. As of yet, I have not had this done... so the jury is still out on whether or not this is my problem.

I had a similar problem. My car would act like it was about to stall out while I was in the middle of driving but then would kick back into gear and keep going. I took it in and it was the input speed sensor.

I have a 2001 Sonata and this past week I have had an issue of the car stalling after driving for 15 minutes. It would stall out while I was driving. I took it in and the mechanic said it is a common problem with Sonata's that the wires under the dash become exposed and rattle against a metal bar. This causes the car to kick into safe mode and shuts down. Not sure if this helps.

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My 00 Sonata 2.4L did this last spring , just driving along, electrics cut out for a minute, then came back on[only ever happened that one time] (Millenium Falcon Moment) with in 2 months the alternator was dead. only cost me about $380 to have replaced.