We closed an S Corp years ago, but turbotax keeps asking for a form K-1. Do I need to keep filing this, and if not, how do I get it to stop?

You can delete any forms you no longer need.

When you open a new tax return in the same account, turbotax auto-creates blank documents for your past tax situations to make it easier to fill them in (like W-2s, charity donation, mortgage interest, and so on).  It sounds like Turbtax is creating a blank K-1.  If you don't have a blank K-1, you can delete it by clicking "review" or "revisit" on the section, then the screen should show a list of K-1s that you can open, or create a new one.  There should also be a delete button next to each K-1 in the list.

You do not need to file a K-1 if you did not receive it.  You can delete the form from this year's return and it will stop carrying forward when you start your new year's taxes.

To delete a specific form in TurboTax Online you can follow these steps:

1. Within your return, click on Tax Tools in the black menu on the left side of the screen.
2. Click on Tools.
3. Click on Delete a Form. 
4. Scroll down to your Schedule K-1 and click Delete.
5. Under Federal in the black menu bar click Wages & Income to get back into your tax returns.
6. Proceed entering/reviewing your return.

To do this in TurboTax Desktop you can follow these steps:

1. Within your return, click on the Forms icon in the upper right of the screen to switch to Forms mode.
2. Scroll down in the menu bar on the left and select your Schedule K-1.
3. Click the Delete Form button at the bottom left of the preview screen.
4. Confirm the deletion then click the Step-by-Step icon in the upper right of the screen.
5. Proceed entering/reviewing your return.