I tell my team all the time that my door is always open. Then I'm in back-to-back meetings, head down, half-answering messages between calls. Someone stops by and I don't even look up. The invitation I keep repeating and the person I actually am are two different things.
More people experience this than they realize.
You keep saying you're available while being impossible to actually reach.
If this sounds familiar, the Library can help you find the bigger picture.