Translation:My love for you is still alive.
No, you do not need both. You can use either or. That said, it is quite common to use both. It kind of supports an idea that something is still going on though it is surprising or unexpected. On je stále ještě naživu = He is still alive, though he is 106 and nobody expected it.
Czech would never use this sentence. Possible is: Ještě/Stále tě miluji. Or: Ještě stále tě miluji. (also miluju)
I don’t agree with you. What about poems? Your proposal also has its own translate.
Stále tě miluji = I still love you.
Ještě tě miluji = I love you yet.