The problem is I had my arbor trimmed too low and I believe it is dead now.
Can the branches be cut so low that they will not grow back?
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Yes that is possible. It's like felling a tree.
Some tree species can resprout from roots or what little bark is left. Some can't. Here are some details: https://www.quora.com/Will-a-tree-grow-again-if-only-the-stump-is-left