Since I'm a sucker for horses, I love this story already. I've put my thoughts in red.
Seventeen-year-old Natalie Miller is as good as dead.
I found this first line a bit confusing. I thought she was already dying. Maybe rephrase to something like 'Natalie Miller might as well be dead.'? At least she thinks so. I'd cut this line. It doesn't add anything to this first para. Her parents practically ignore her, her teachers at school don’t realize she’s there, and even the bus driver manages to leave without her every day.
Maybe some more concrete examples could be used here? I don't feel like I get enough of a sense of Natalie's unhappiness in this para to carry the suicide in the next. Does she have friends? Enemies? How do her parents ignore her (Do they never talk to her/look at her, etc)? I think build the picture of a depressed/unhappy teen as much as possible in this first para. I know it's tough in such a short space!
When a flyer for a hip
The word 'hip' is a bit old school (at least it is in Australia), so it could jar readers of YA, unless it's a character building device to show Natalie's uncoolness? party somehow ends up in her backpack, she decides this is the one time she will do something that no one will ever forget: commit suicide.
I think this needs more of a link. Why is the party the perfect opportunity to commit suicide? Is she going to do it at the party? Natalie plans her perfect out and when the time comes to swallow the pills, something goes wrong. She doesn’t die.
I like how you've said not dying is something going wrong. It's a good insight into the character's mind.
Natalie is given a choice by the hospital psychologist and her parents
, who keep calling her suicide attempt an “accident,” to either spend six weeks in a psych hospital or a rehab horse camp. With the help of a horse named Penelope and a boy named Gabe, Natalie’s choice forges a love for herself she’s never known.
Does it just forge a love for herself? Does she also build friendships she hasn't experienced before? This wording feels a bit vague.
A Horse Named Penelope is complete at 75,000 words and is a stand-alone Young Adult Contemporary novel.