I wonder: what does it depend on that a person acquires or not a "neutral accent" in a foreign language?
In general, our accent makes us being remarked within a community whose native language is not yours. This is kind of "cute" because it makes part of who we are and it has nothing to do with your language mastering, that actually can be pretty good.
My experience in French is quite the opposite: natives might first think I'm a retarded French speaker when I make a mistake. After that, they suspect I might not be "one of them" and they take the risk to ask THE question: "Where are you from?" (the answer being 'Mexico'). Just then... I know what is coming next (I have a pattern now): "Oh! you have no accent".
Not knowing if I'm supposed to say "thanks?" or not, I just adopt a nonsense laugh and continue my life.
What is your experience with your other languages? Is it one of your goals to work on your accent or not? What is the feedback you have received from natives and how has it influenced your speaking?