Caring about characters

One of the most difficult and frustrating pieces of feedback for a writer to get is this:
"I didn't care about the character(s)."

I have junked manuscripts based on such feedback. It's such a fatal, fundamental and pervasive flaw. If the reader isn't invested in the story, game over.

But if such a flaw is ever fixable ... how? What makes readers care about a character? What makes you care?