Characters are busy too! They may be at a concert, on a spiritual retreat, photographing stunning landscapes, or flying to a new city to explore the sights! They will return when they have the chance, either in a few minutes or sometimes a few hours.
If a character is completely greyed out from your message screen, it may take them longer to reappear. Some characters may be taking a break from Lovelink, but don't give up hope!
Don't want to miss their message? You can opt-in to get a notification when they come back online!