Sorry not really an idea what it could be. But as you wrote you were coasting when it happened, so I don't think the engine was turned off. Otherwise the car would decelerate abruptly when there's no ignition and a gear is in (like running out of gas). On the other hand, you said you restarted while doing 40mph... therefore the engine must have been off.

If the engine were running but had no acceleration, it could be a malfunction in the gas pedal sensor. But this wouldn't make a link to your rough idle.

Do you always have rough idle or only sometimes?