I don't think there is any downside to heating it again. Note that the brown bits come from milk solids so if you've already removed those (e.g., scraped them off), then you're just stuck with clarified butter.
Also, for the next time you try this: the way its boiling changes as it runs out of water—and that's when the bits will start to brown. It's aroma will also change. You'd probably also see the temperature rise above 212°F/100°C if you had a candy thermometer in the pot (not sure, haven't tested as its not required). Those are the primary indicators of doneness, not how long its been cooking for.