After aliens attack a process is created that bestow superpowers to soldiers but at the cost of giving them a four-year lifespan. When an enhanced man learns of a new pending offensive and a secret that may end the war forever he must fight his way back from behind enemy lines or humanity will fall.

The first sentence in the logline can be cut, it's not a part of the plot and only describes the back story. That could perhaps make for a good origin story but should not cloud the current plot.

Secondly, consistency in your descriptions is important, if he is a soldier then describe him as such throughout. I also find the description "...doomsday device..." funny, it's something I'd expect Austen Powers to go after. Can you be more specific with the weapon's description? Perhaps a biochemical toxin or a pandemic causing something or other.

For example:
After discovering an alien pandemic causing weapon threatening humanity an enhanced soldier must destroy it before the process that gave him his powers kills him.

This is still a little off, but maybe closer:

After aliens attack a Process is created that bestow superpowers to soldiers but at the cost of giving them a five-year lifespan. After discovering a doomsday device an enhanced man must destroy the weapon before it can be unleashed and before the Process that gave him his powers kills him.

The working title for the story is "The Process" -- that's why I capped it. Probably doesn't really need it for logline purposes, though...

The inciting incident is the soldier learning about the impending destruction of humanity. It seems a bit unlikely that a new offensive, as oppose to the previous ones, would spark his fear for mankind. It may need to be a specific item, like a weapon of some sort, that scares him into taking action. Otherwise, it is a bit vague as to what he will do as an individual on his own even with super powers.

Secondly, what are the super powers? Is he strong? Fast? Can fly? Can he control other people's minds?