"when asked if I get periodic payments from my NYS Retirement System pension, I select YES, but it will not remember that after I hit SAVE. "
Actually, TurboTax does remember your answer; it just looks like it doesn't because it resets the answer to No every time you enter the page. If you don't reenter the screen, your answer is still be Yes.
Why does it do this? Because the designers feel that some questions are so important - and which change the path of the screens to follow - that they want you to reconfirm your answer each time you enter that screen.
"That results in an error when I try to deduct pension from NYS taxes."
The Yes/No answer issue is not the cause of any error above. Instead, there has been a different issue with New York pensions. Some of them were not being marked correctly as to the type of retirement income it was.
I believe that this issue has been resolved. If you are using the Online product, it should be OK; if you are using the CD/download product, please make sure that you update your TurboTax software.
If your issue is not resolved, then please tell us what the issue is, since we in the Community cannot see your private tax data. Help us help you.