Give up or keep writing?

Writers write.

But the harsh reality of the situation is that not everyone will want to read what you write. Whether it is timing, luck, the economy, or the population just isn't ready for your type of story, you have to realize that you may never sell your story.
If this stops you from writing, then you aren't a writer.
Perseverance makes a writer. The will to keep slogging through. To write the next story. And the next one no matter how many rejections or negative responses you receive.
Why?

Because, writers write.

The only way to get better at the craft is to keep writing. The first story most writers churn out is crap. Yeah, yeah, it's the book of your heart--so get over yourself already. That was your selfish novel. Now you need to concentrate what the rest of the population is interested in. Does this betray who you are as a writer. No, it makes you realistic. And don't write what is currently on the shelves--remember, those books were bought one to two years ago!
Publishing is a BUSINESS. Everyone is out to make money. The way to make money is to appeal to a large portion of the population. This doesn't mean you have to compromise your writing self. Write what you love. And once you discover your voice and let it truly shine through, then they will find you.

Write on!