So if you use a field hospital a second time on a level the first one disappears. That kinda sucks.
Well, I can see both sides. If you can deploy several field hospitals at the same time you can stack their effects and ultimately get some of those really expensive territories for free. But then again, if you spend literally days to cool-down your artifact several times to accomplish this, then you should be rewarded for the time and effort that you put into it. So, all in all I'm on your side and would like them to stay until all neighbors are claimed.