There isn't a single person I've coached over the years - and I'd include myself in this group - who've lost their confidence at one point or another. It might be a momentary slip, or something that lasts longer than a few weeks. But it happens. The important thing is to call it for what it is, realize it's natural and probably inevitable, and take appropriate action.
Here's another excellent post from Dawn Lennon's blog Business Fitness, entitled "Self-Confidence Lost? Five Steps to Getting It Back." Her steps are wise and practical.
If I may add a personal point to this, I'd offer a favourite retort from my Grandma Eklund - the doyenne of common sense. Other people's opinions of you are none of your business.