I read it in English five or maybe even ten years ago. The protagonist is a young guy, and he meets a girl. And a giant bird shows up. Basically, the city is sort of frozen in time. The girl works for the city's government. And there is a scene where here boss shows her around the city, and they visit a hospital with pregnant women. And basically they are unable to give birth. They've been pregnant for years. They were pregnant at the time, that some kind of mysterious event happened. So, basically if you were pregnant during the event you stayed pregnant and if you were asleep, then you stayed asleep. I think that maybe everyone was immortal as well. Appreciate any help in finding this manga. Thank you.

I managed to figure it out on my own. It's Betsuma. Thanks anyway.