After having looked at a few snippets where this is used through google the closest I can think of in meaning in English would be "Not yet ready to give up", and if not as antiquarian in your language as I am DGaleano pointed out a nicer usage: "Not reason enough to give up" (though for literary purposes I like "not having shuffled off this mortal coil").
After reading up on this, I have been thinking about translation principles (notably that directly literal translation usually misses the meaning), so
Sin muchas esperanzas, porque el teléfono de la vecina donde la
llamaba seguía cortado y no tenía la menor idea de dónde vivía. Pero
no era para echarse a morir, qué carajo, dijo, te llamo en una hora.
Literally translates to:
Without much hope, because your neighbour which was called cut and had
no idea where she lived. But it was not to lie down to die, what the
fuck he said, I'll call you in an hour.
However when reading the Spanish, the following feels more correct:
"He didn't hold out much hope, as the call on the neighbour's phone
could cut out anytime and he had no idea where she lived. What the
hell, it won't kill me, I'll call you in an hour."
And I know it is not the literal exact copy of the snippet above, but from that snippet I think this holds better to the meaning. I will get the book and read it, see how I manage with translating the quote once I have it in context.
I will try and find some books at home to quote from properly.