Guys, I'm having similar issue. 2000 V6, Automatic, randomly dyinig, taking 10 minutes before it wants to restart. Honda dealer diagnosed as bad Ignition switch and wanted $460.00 to replace. They also said my VIN was not part of the Ignition Switch recall.
I installed a Beck-Arnley Ignition switch myself which worked for about a week, then problem returned. I thought maybe I got a bad one and replaced the Beck-Arnley with an Intermotor brand. The problem persists. Another piece to the puzzle is that if I put the car in Park at a long light, it won't go back into Drive.....I have to depress the recessed override button to get it out of Park. This issue seems related to the Ignition switch as it won't go into Neutral after the engine dies (with Ignition in Run position and foot on brake). Any thoughts ?

 

I moved your post into a separate new thread, as your issue seems different and this way you'll get more specific help.

 

Since you already replaced the ignition switch twice and also have a problem shifting out of Park, your issue can possibly be related to something else, such as a faulty Powertrain Control Module (PCM). The PCM is the car's computer.

When the car dies, does the dash lights, etc. stay on? If the dash lights, and gauges stay on, it probably is not due to the ignition switch.

This is a description of how how the shift position interlock works:
Battery voltage is supplied at all times through fuse 47 to the brake pedal position switch. With the ignition in ON (II) or START (III), battery voltage is supplied through fuse 9 (in the driver’s under-dash fuse/relay box) to the shift lock solenoid. When you push the brake pedal, battery voltage is applied through the WHT/BLK wire to the PCM. If, at the same time, you do not push the accelerator pedal, a low voltage signal is sent through the RED/BLK wire to the PCM. The PCM then applies voltage through the WHT/RED wire to the shift lock circuit in the driver’s multiplex control unit. When you move the A/T shift lever from the PARK position, ground is provided to the shift lock solenoid. The solenoid is then energized allowing the shift lever to be moved from the PARK position.

 

Good stuff RedBull - thank you !
Yes, the dash functions remain active during these simultaneous periods of engine no-start/AT shifter lockup. Wait 10-15 minutes and she fires right up and shifter moves out of Park normally. Does the aforementioned confirm PCM to you ?

 

It doesn't necessarily confirm the PCM is the cause; but, there is a possibility that it may be the cause.

You can always open up the PCM and take a look to see if there are any damaged resistors, capacitors, board burnt, etc. Even without seeing anything visually, the PCM can still be faulty. So can't be sure if PCM is faulty or not from visually inspecting if there isn't anything obvious. Also, check the wiring and connections at the PCM.

The PCM is located under the dash, center console area.

 

Took it to dealer....it wound up being Relay Assembly 91600, part # 39400-S84-003....cost $81.59. Hope this helps someone down the road.