I hate to come off as a nymphomaniac, but...

[HerenIstarion]

how can a girl hope to beat the other woman giving up her immortality for the man in question, especially when she doesn't have immortality to give up

In many different ways, to be honest, in case man is one of not so firm morals. When one is going to give up something for you, you may be even frightened by the option, and try to run away (one of the possible, mind you, options)

But again, as somebody said "love is enough", but another one answered "it is not". I vote for "it is not" option, beggin your pardon, if you follow my meaning...