Rudderless since returning from the Gulf, a sardonic veteran’s hapless life gets a bump when he befriends a youth in need of a mentor, but in order to save his budding relationship with his young protege’s mom he must shed his old skin and become the man everyone, including himself, needs him to be.

In a comedy with kids, the lead is usually forced together with the kid, leading to the lead characters discomfort and comedy.
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"When he crashes into a single mom's car, a sardonic veteran reluctantly agrees to mentor her incorrigible son in return for her not notifying his insurance."
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Though this sounds like a great story, the logline is a bit to convoluted for me to really get a good image of the movie in my mind. I agree with the other comments, simplify as much as possible while telling us who the protagonist is, what their goal is and what the obstacle is.

Hello, the movie can be interesting,
for the logline I reiterate the comment above: it would be better to avoid backstory (the Gulf), make it shorter and clearer, focus on the main goal, and give a better descritption of the plot. What is the inciting event?
I strongly suggest to try to include some fun in the logline, because in reading it I thought of it as a very serious movie like Gran Torino. Where's the irony? What generates the fun in your comedy?

I don't know if any of this is true to your story but i suggest something like :

"When his new friendship with a young fragile boy is jeopardized, a sardonic tough veteran must shed his old skin to truly become his mentor."

or

"When a sardonic tough veteran befriends a young fragile boy, he must shed his old skin if he wants to truly become his mentor."

Good luck with the contest