From my own personal experience....having both lacinato and red russian kales in my raised beds...at least three of the plants are from last year's harvest...and overwintered through snows, etc...and then grew like crazy this spring and we are still picking from them. It's crazy how long we have picked from those plants. This year we planted two rows , one of each, and we're still eating, but l like you, their production has slowed...but I am going to try leaving them in the garden and see what happens in the fall.

I'm also growing Lacinato and Red Russian kales in 1 of my raised beds. Started them in early spring and they are doing amazing still. I have them in an area that gets some shade and they thrive there. I also covered the bed with a summer-weight row cover to keep insects out.

I wouldn't pull them unless you plan on using the space for another vegetable. They will absolutely keep producing and then when it really cools down, the kale will sweeten. Kale is very cold-hardy.

Do the center stalks where the leaves grow from get kind of tall over time? So that the newer leaves are not as close to the ground as the original leaves? I ask because I pulled some kale this summer that was doing that, and I thought it was bolting or getting ready to bolt. Both lacinato and red russian.

Yes, the stalks do get taller. These still haven't bolted. Must be because of their shaded location. I might just leave them until winter temps kill them.

Actually, kale is a biennial. It won't bolt until after overwintering(should it survive), in the following spring.

Even though kale is a biennial it can bolt prematurely if it is in poor conditions. It doesn't necessarily have to overwinter. For example, it can flower when only a few inches tall if left in its original seed module and not transplanted.