I assume you're using CS6, 3.6 comes with CC, 3.2 comes with CS6. Are the SDKs by chance still in recycling able to be restored? If not just re-download 3.2 (what it expects to exist) and put it back in the AIR3.2 folder. That's the easiest. You could also try the preferences reset but it may not fix that issue and you've already said you don't want to lose your settings.
AIR archive downlods:
In the future, as I'm sure you know now, just jump in that panel and remove a SDK before you delete it. You'll notice the panel is quite static. If you update the version of an existing SDK (3.9 to a newer 3.9) it retains the old version number unless you delete it and re-add. It doesn't update itself as well as it could. As a general rule of thumb I never remove the default SDK or Flash Player version a version of Flash Pro comes with.
Thank you for your tips and guidance, especially the link to the legacy packages and your "rules of thumb".
I could get rid of all intermediate versions (3.5, 3.6, 3.7, 3.8) after I downloaded those packages, added them to the project folder, took them off the SDK manager list in FLASH Pro and then deleted them.
And after I also added the 3.2 and 3.4 versions I could add the 4.0 beta and there are no longer message windows popping up.
Since SDK manager does not offer to take 3.2 and 3.4 off the list (the "-" is greyed out), I'll follow your suggestion and just keep those.
So I'm OK for the moment.
And yes, I am using CS6.
Glad you got it resolved and if you're all set please mark helpful/correct so we can filter unanswered questions.
You're welcome and good luck!