It's hard to see from your pictures. But, if there is damage to the shoot apical meristem, your seedling will not form any new leaves or new growth. Sometimes soil born plant chewers will chew this part of the plant off. I've had it happen to 25% of my bush beans this year. Several folks here had pill bugs do exactly what you are seeing and some even chewed the seedling from the base as well.
the little first leaves after i blew the picture up look a brown on the tips (first picture).could be damage of rot/mold ...or as @TimJ has said it could be insect damage ,,,..mac,
I'd say a week or so. It won't hurt anything to keep it alive. I don't have a shortage of seeds so I always plant a few and toss the weaker one.