Fallout – How to get more pet chests in Fallout Shelter

The only thing which could explain it (besides a bug) is that you may missing some electricity or water. If you haven't enough electricity your food and water supply will fall down and maybe collapse. This will increase the radiation of your dwellers. In some cases they may die on this.

Otherwise, I would say it could be a bug. I've had a situation which was nearly the same. In my case electricity was too low, which leads to the situation I described above.

No, you do not lose progress by swapping Dwellers out of training. They go back at the same remaining-time as they had when they were removed from the room.