Just to clarify, I wouldn't mind an immortal Superman and I think such a Superman is very in keeping with the concept and even the character. The idea of a man forever working for a better future no matter what. Our eternal never ending idea that will outlive us. I wouldn't even mind it if he gained immortality from an outside source (depending on the source I rather like it actually).
My only thing is that I'm not down for such a selfish reason for it. It's cowardly of both characters regardless of the rational IMO. She's so scared of being without him that she wants to use her love to keep him immortal? Nah bro, not my thing. That's at least how it seems to come off given the way it's being explained to me.
Now I'm a VERY flexible person when it comes to a lot of this regarding comics and fiction. I like things that have thematic importance and symbolism and all that crap, so I'm open to a story like this where Wonder Woman ask this of our Superman and he says yes. The thematic side of it screams two scared gods that don't want to let go because of personal self centered reasons (as a couple you are essentially one when it comes to things like this IMO so it's selfish).
The story wouldn't have to paint then in the harsh light that I seem to be setting but that would be part of it. The irony would be the closer to "godhood" they get the more scared and human they really become. This would make for interesting reading and comes off as an Alan Moore story ala Twilight of the Superheroes, For the man, and Whatever happened.
So In the end I'm down for such an idea. But on personal preference and principal I'm not for it and I think it's not Superman regardless of the who's his gf.