I have to check for leaves but I know there is a problem with flowers and fruits than can really kill the tree instead of just rotting and falling. I will work on this but meanwhile you already can manually cut outer branches by clicking on them (it's in the doc in Tips section but you know i struggle a bit to have a simple and clear doc..), this is not the most convenient but it can really save your tree!
I'll also add a way to reset a level, maybe it could give some resource (like wood) depending on the current tree in the level to make something with it :)
Thanks again!