Odds of Hanging On
If you've got ten or fifteen years doing this job, you're all set. The doctor you work for will seriously rely on you by then, or he'll retire and the person taking his place will need someone qualified. Yeah, that would be you.
Again, speech recognition software may lower your rates and change the business, but it won't entirely put you out of a job. At least not until Skynet takes over...and we'll all be screwed then, so it won't matter much.