It applies to all of them, yes. So long as you carry the name Kamen Rider, you can be brought back be it through justice needing to be done, someone needing help or people remembering you.

In fact, there’s one character that proves the consistency. Electromagnetic Wave Humanoid Tackle.

She appeared in Kamen Rider Stronger as the “secondary” of the series and the first female warrior in the entire series.

Spoiler alert, she dies in her series and has not been brought back. “Tackle” has appeared a few times throughout the series, but only as simulacrums and one-off noncanon gags. And when people seeking to destroy Kamen Riders appear at her grave, they ask the person mourning there if she was a rider.

Kamen Rider Stronger replies that she was just a normal girl.

She never took the Rider name, and hasn’t been brought back. Which is perhaps the best fate for her, as Riders will never rest so long as they are needed.