I have some personal experience that suggests otherwise. A close relative of mine aspired to live in France for most of her life, and after a divorce she decided to pick up and move to Paris at the age of 48. When she first moved her French was quite bad, and Parisians would regularly switch to English when they heard her broken speech. Fast-forward to 8 years later and she is now fluent to the point that she's able to take on clients to her psychotherapy practice who speak only French. Her accent could use some work, and it took 7 or 8 years of complete immersion, but I don't know that there's any hard "limit" per se, to what someone can learn at 50 — it just takes longer.
