I know that "しない" means "not do", and "いられる" means can exist, but I can't put it all together.
My best guess is that it means "The mind/spirit that could be here won't do it".
～～気がする means "I feel like~~" "I get the feeling that~~". So ～～気がしない means "I don't feel like~~" "I don't get the feeling that~~".
To break it down...
もう～～ない not anymore
ここにいられる can stay here
気がしない don't feel like...
Putting them back together:
I don't feel like I can stay here any longer.
It means "I don't feel like I can be here any more." See: https://selftaughtjapanese.com/2014/01/06/use-your-energy-useful-expressions-in-japanese-which-use-ki-%E6%B0%97%EF%BC%89intermediate/