If they are like other birds and go to "bed" at night, then no. The only thing I would rely on would be a livestock guardian dog. But they require a real commitment, secure fence, and training. If you aren't willing to put those in, it would be better to simply reinforce your chicken enclosure.
Do you have a pen or coop they go in at night? You could get a electric fence and put around the perimeter about 5 inches off the ground. Every since i've done this, i've never lost any birds at night. Before hand, even my dogs wouldnt stop it. Predators are just too sneaky and quiet, and by the time the dogs hear them, they are already inside the pen, or have killed something.
Yes, I have three coops actually! We have one corn crib for one for the hot summer, but a mink killed half of my hens, including my silkie hens. we have to put them up in the winter coops so they are safe, and its extremaly HOT!! I feel so bad for them. My dad was talking about getting an ostrich to put around the coop, but that wont work! We are out of ideas because we cant afford another coop unless someone sells a shed or large coop for cheap! Thanks for the fence idea though, i just dont think it will work for a Mink problem..
What if you built a dog run to frame the chicken coop? Imagine the coop and any attached run as the inner rectangle/square, with another one on the outside, with a dog house. I'm just throwing out an idea...I've never actually done this.
Our winter coop that the big chickens are sleeping in is built under a barn, they dig under the barn, plus they can climb! One night we had the baby monitor on and we herd my seabright rooster screaming bloody murder so my dad grabed one of our guns and ran in the coop, it had him by the neck plus he grabbed my rooster Ebby and had him by the nech too. He shot and it climbed a big wooden beam in seconds. It came every night and killed my baby chicks, hens, and bantams.
So we have to but all the chickens either in cages, or hot winter coops. Its really sad.
... We do not know what to do other than build two more coops, which is exspensive!!
if the basset is still young, active & healthy enough, teach it to run the mink. hunt them and kill them before they get to your birds. do that WHILE you work on a solution to prevent predation. also learn trapping techniques for when you can't actively hunt. while not the best choice mink can be caught in cage traps. if you can secure them from other animal 110, 120 or 160 body grip traps would work best. get a few of those bird eaters and you could have some super warm winter gloves.