Can the immobilizer on a 1999 Accord stop the engine after starting?

A couple of days ago my engine just stopped while on cruise at highway speed. The engine had been running quite happily for about an hour.
The only light on the dashboard that lighted was the green immobilizer
light which is the reason I look in that direction. I turned off the ignition and restarted the car immediately with no problem. The problem has only occurred once, so far.
My concern is that this may be the start of some issues with the immobilizer. I am guessing that either the immobilizer receiver or the control module is failing. Is there any way to find the problem before it fails completely and leaves me on the road with an immobile car?
Thanks.
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LakeGator wrote:

your car was subject to the great ignition switch recall. look into that before you spend time on anything else.
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I agree with jim beam (before I even knew your vehicle fell into the recall status) - it sounds like an interruption of the ignition, which got the immobilizer on its high horse.
Mike
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wrote:

Thanks very much for the excellent and simple advice. Off to the dealer we go on Monday. (-:
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