Possibly cutworms, I had this happen to me one year, one pole, 8 plants, almost to the top of the pole. All vines had been neatly cut off right where they emerged from the ground, it was cutworms in my case. Sorry I don't have a recommendation for you, most insecticides have been banned here in B.C. Maybe someone else will chime in with a solution. If planted around a pole maybe give the seedlings a collar, toilet paper tubes might work.
Annette

I even had this happen with some kind of small bird. I planted some Tarahumara Purple Ojos in a bed, at work, and when they came up, I actually watched through a window, as a little bird flew down and snipped them off at ground level. If I hadn't seen it, I wouldn't have believed it.

George
Tahlequah, OK

If that bird was a finch, I believe it. They have ravaged several of my vegetables over the years, especially peas and chard.

I think it was a finch.

I was gone for the month of July and have about five surviving bean plants. Here's a link to cutworm prevention I will try next year: http://www.veggiegardener.com/tips-for-preventing-cutworms/