No one noticed that the genitive case here is used not due to the negation, but due to the verb itself.

The verb "хватать (imperf.) / "хватить" (perf.) meaning "to suffice, to be enough" always requires genitive, even if not negated.

Мне хватило твоих денег. - Your money were enough to me.
Мне этого хватает. - This is enough to me.
Им вполне хватает вашей помощи. - Your help is quite enough to them.

This verb is impersonal, it does not have any subject. (The dummy pronoun "it" as in English is assumed but not used in Russian).
The syntax of those constructions can be roughly rendered in English as

Мне хватило твоих денег. - To me (it) was-sufficient-amount OF your money.

In negative forms the genitive is still preserved:

Мне не хватило твоих денег. - To me (it) was-insufficient-amount OF your money.

So, "Просто жизни не хватит для этого" = "Для этого просто не хватит жизни" (more English-like word order) = "For that, just (it) will-not-be-sufficient-duration OF life".