According to the in-game guide their health is based upon their level. With out actual numbers and since the dangers seem to scale along with your dwellers though, this is a bit hard to qualify from an end-user standpoint.. but that is what the guide says leveling does.
Research! I had a room with many different levels and I rushed it until I failed to get the following screen shot
This shows the same damage being done to different level players and there is a clear difference over the length of the encounter. So level up those characters! It keeps them alive longer!
I'll be honest and say that I've never come across this, but I have stumbled across some small glitches before, and I'd say that is what this is. Since athletic rooms have a maximum capacity of 4 dwellers, and you said that there are currently 7 people in the center, I wonder if it will max out at 8? However, you also mentioned that no one has left the center; can they leave if you reassign them? If not, I would definitely say that it is a bug.
I used to play it on BlueStacks (PC emulator) which caused several small issues from time to time but never something like this. However, I assumed that this was due to running it in an emulator. I'd probably try reassigning all of the dwellers from the old room, and then reassigning some others to the rooms. If that fails, I would probably try destroying the new athletic center and rebuilding it (if you haven't), and seeing if that solves the problem. That being said, it seems that it likely won't, so I would also suggest destroying and rebuilding the old one (assuming that you can reassign the currently inhabiting dwellers, have the coins, and the room isn't the only tie between two rooms).
While this is much less than satisfactory, I cannot think of a reason that this would be occurring. Could you by any chance post a picture of your vault (if you want)? Not sure if that will reveal anything, but probably can't hurt. Good luck!
TL;DR
- Reassign all dwellers from the old room, and then assign other dwellers to both rooms
- Destroy the new room and rebuild (loss of coins)
- Destroy the old room and rebuild (loss of coins, possibly impossible)
- Destroy both rooms and rebuild (bigger loss of coins, possibly impossible)
Note: If either room is the only connection between two others, that will be a problem (obviously).
Best Answer
Really? The timer is on there. He is travelling to the mission. It will take 3 hrs 50 mins. That is why he hasn't left yet. He will do the mission, it is just a graphical bug.