According to this article in the Asahi, the plane is still there awaiting a spare engine. Earlier they reported the passengers had to stay on the idled plane for 9 hours but here it says they waited six hours for the replacement flight to land and a further three before they finally took off at 9:35pm. The reason given by Delta for no permission to disembark is now quoted as 'inclement weather' and 'lack of available facilities'. This is the first time in 11 years that a civilian passenger flight has landed there.
Normally a flight will make for the nearest base with support staff, but in this case they were mid-Pacific so chose land at Iwo Jima and had to fly Delta maintenance staff out from Narita, according to the Sankei news group.
Asahi
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デルタ航空によると、基地内に乗客が待つ場所がないうえ、悪天候もあり、機内で待機させたが、体調を崩した人はいなかった。エン ジン交換のためトラブル機は硫黄島に残している。