As long as there is no threat of frost you can let them keep going. Even if a frost is threatened you can cover the plant for the night and uncover in the morning and let it keep going.

Basically it is your choice. If it is still producing and the weather permits why pull it?

Dave

I agree with Dave.

There is a chance for the tomatoes on the vine to get ripe, either on the plant or inside, on the counter. However it is very unlikely for the flowers to have a chance even if you continue having a long Indian Summer up there.

Sey

I'm somewhat in a similar situation with my high tunnel tomatoes ( and another with peppers). I had heat from wood stoves on for these past 3 nights just to keep going for a final farmers' market on Friday but it will be a hard choice to remove "Life support" after that. The numerous blossom clusters are so begging even though it is evident that not only don't they have a future but neither do the literal tons of fully formed unripe fruits. Although customers are asking that I keep growing for an indoor winter market it is just not practical for me.

In your situation with potted plants why not let the weather guide your decision. Keep the plants producing as long as you are comfortable in doing so. Good fresh salad tomatoes in December are hard to come by in NYC.