All writers must have some inner drive to put stories on paper. That's been my experience anyway. Rejection is the norm. I've spent the last six months just trying to find an agent--without much success. Something must make you keep going. On top of the inner drive, I would think every writer's experienced a few things on the outside to motivate him or her--if not, seek them out, they're good. For example, you met, spoke, listened to an influential writer at a conference or convention, you received a real--on the phone--reply from an editor or agent, offering advice--or even better, asking for the rest of the ms.
Here's one of mine, in the form of a rejection letter. This was the summer of 1981. At the time my favorite authors were Tolkien, Herbert, Heinlein, Poul Anderson, Gordon Dickson, Robert E. Howard, Andrew Offutt and H.P. Lovecraft. I was just out of high school and I sent off my very first query letter to Offutt, who'd been editing a fantasy anthology called Swords against Darkness. I'd just finished reading his latest addition to the Cormac Mac Art saga (can't remember which one, but When Death Birds Fly was always my favorite). My mom persuaded me to send a query, see if I can get a story submitted. What's the worst that can happen? I wrote out a long letter, described my story and character, what he did, some sort of crafty Odysseus type hero, if I'm remembering him right. Being a total newb, I mucked it up pretty good right from the start, calling the anthology, Swords of Darkness instead of Swords against Darkness. (Yeah, and didn't Heinlein write one called I Will Fear No Good?)
Not only did Andrew Offutt reply, he sent me a full page letter typed on one of the page proofs to a Thieves World story. It still amazes me that a real author would take the time to write a letter to someone just starting out. Take a look.