I think there is a valid analogy to be made between beans and tomatoes. Bush type beans are analogous to determinate tomatoes, which basically die after setting a crop no matter what you do to them. The pole beans are like the indeterminate tomatoes, they can keep going a long time if cultural conditions allow.

An update, I'm picking a grocery bag full every day since about the 18th. I'm eating some and they are just as good as they were with the first crop.

I've been giving them to the food bank and they are very glad to get them. They haven't been getting any since mid July.I drop them off every day on my way home from work.

They have gotten to know my truck and when I'll be arriving, so I'm getting curb service now! LOL