I just went through the same thing with a mink 2 weeks ago. Sadly once they know you have birds and have made a kill it will keep coming back. The one we had was coming middle of the day. I caught it in the act and once I had secured my survivors I borrowed a live haveaheart trap. I used my poor dead bird as bait. Caught that mink within 2 days. At that point a pellet gun was our best solution.