I created a faucet (I won't share the link).
I topped it up with 1,000,000 satoshis and put in some ads. By the time it was emptied out, I was only able to make a total of 13,000 satoshis from advertising revenue.
The most popular faucets such as Freebitco.in are probably quite profitable for their owners but it wouldn't surprise me if most of them never make a profit. The market is pretty saturated enough as it is.
They also earn money from donation & captcha too
They could earn extra money if they share other faucet site with their refferal links
Anyway, make money from faucet is bad idea
Who the hell actually donates to faucets? I see no logic in that. And the amount of money operators get for every completed captcha is tiny fractions of a cent.
Gavin's original faucet got quite a few donations. Of course, the situation back then was very different compared with today.