when I can make someone smile after they were feeling sad
When I give time, when I can make someone smile after they were feeling sad, it's as close to healthy as I ever feel.

Why use past progressive tense here (were feeling)? I think, the other two work perfectly fine here.
What's your opinion?

...., after they feel sad,...
...., after they felt sad,...
...., after they were feeling sad,...

Question

when I can make someone smile after they were feeling sad
When I give time, when I can make someone smile after they were feeling sad, it's as close to healthy as I ever feel.

Why use past progressive tense here (were feeling)? I think, the other two work perfectly fine here.
What's your opinion?

...., after they feel sad,...
...., after they felt sad,...
...., after they were feeling sad,...

Answer

You need to use "were feeling sad" because it is a continuous state that is interrupted by you making them smile. Examples that are all in the past are more obvious:
I was sitting in the bath,  when the telephone rang.

You cannot use present because the adverb indicates a past event (after)
You can't use present because then the sadness would be a permanent state.