A permanent retainer may be left in for mikveh immersion. However, you must take great care to clean the retainer very well to ensure no food is stuck in it or between it and your teeth and you should check to confirm that the retainer is securely attached before each immersion.
Note that there is halachic debate about when a permanent retainer may be left in for immersion: in all cases or only when medically advantageous. Our site's supervisor, Rav Yehuda Henkin, agrees with the lenient opinions allowing immersion with a permanent medical retainer even when the permanent retainer does not have a medical advantage over one that can be removed regularly.